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Research Interests: Mathematics, Applied Mathematics, Functional Analysis, Theory Of Computation, Control Theory, and 10 moreHeat Transfer, Pure Mathematics, Distributed Control, Numerical Analysis and Computational Mathematics, Optimal Control Problem, Vector Space, Differential equation, Boundary Value Problem, Electrical And Electronic Engineering, and linear operator
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Various aspects of the theory of second-order differential inclusions attract the attention of many researchers (see., e.g., [1, 2, 6, 12, 18, 42, 46, 47, 68, 70, 97]). In this chapter we consider the boundary value problem of form... more
Various aspects of the theory of second-order differential inclusions attract the attention of many researchers (see., e.g., [1, 2, 6, 12, 18, 42, 46, 47, 68, 70, 97]). In this chapter we consider the boundary value problem of form $$\displaystyle{ {u}^{{\prime\prime}}\in Q(u),\;\;u(0) = u(1) = 0, }$$ (4.1) for second-order differential inclusions which arises naturally from some physical and control problems. Using the method of guiding functions we study the existence of solutions of problem (4.1) in an one-dimensional and in Hilbert spaces.
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In this section we present the guiding functions method for studying the periodic problem for a differential inclusion in a finite-dimensional space.
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We suggest new methods for the solution of a periodic problem for a nonlinear object described by the differential inclusion x′(t) ∈ F(t, xt) under the assumption that the multimapping F has convex compact values and satisfies the upper... more
We suggest new methods for the solution of a periodic problem for a nonlinear object described by the differential inclusion x′(t) ∈ F(t, xt) under the assumption that the multimapping F has convex compact values and satisfies the upper Carathéodory conditions. We also study the case in which this multimapping is not convex-valued but is normal. The class of normal multimappings includes, for example, bounded almost lower semicontinuous multimappings with compact values and mappings satisfying the Carathéodory conditions. In both cases, a generalized integral guiding function is used to study the problem.
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In this chapter we present a new approach to extend the method of guiding function for differential and functional differential inclusions in Hilbert spaces. The results in this chapter were partly published in [100, 108, 109].
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Preface.- S.-N. Chow: Lattice Dynamical Systems.- R. Conti, M. Galeotti: Totally bounded cubic systems in R2.- R. Johnson, F. Mantellini: Non-Autonomous Differential Equations.- J. Mallet-Paret: Traveling Waves in Spatially Discrete... more
Preface.- S.-N. Chow: Lattice Dynamical Systems.- R. Conti, M. Galeotti: Totally bounded cubic systems in R2.- R. Johnson, F. Mantellini: Non-Autonomous Differential Equations.- J. Mallet-Paret: Traveling Waves in Spatially Discrete Dynamical Systems of Diffuse Type.- R.D. Nussbaum: Limiting Profiles For Solutions of Differential-Delay Equations.
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The parity as an invariant for detecting bifurcation of the zeroes of one parameter families of nonlinear Fredholm maps.- Continuation principles and boundary value problems.- Topological degree and boundary value problems for nonlinear... more
The parity as an invariant for detecting bifurcation of the zeroes of one parameter families of nonlinear Fredholm maps.- Continuation principles and boundary value problems.- Topological degree and boundary value problems for nonlinear differential equations.- The fixed point index and fixed point theorems.
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We give a new definition of the relative topological degree for mul- timaps compositions of approximable multimaps and continuous map. We apply this notion to prove an existence result for variational inequalities of Stampacchia's... more
We give a new definition of the relative topological degree for mul- timaps compositions of approximable multimaps and continuous map. We apply this notion to prove an existence result for variational inequalities of Stampacchia's type in finite dimensional vector spaces. Finally we obtain the same results also for multimaps compositions of selectionable multimaps and continuous map. Mathematics Subject Classification (2000). 47Hll, 47H19, 49J40.
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ABSTRACT The existence of a periodic solution to nonlinear ODEs with p'- Laplacian is proved under conditions on functions given in the equation (not on the unknown solutions). The results are applied to a relativistic pendulum... more
ABSTRACT The existence of a periodic solution to nonlinear ODEs with p'- Laplacian is proved under conditions on functions given in the equation (not on the unknown solutions). The results are applied to a relativistic pendulum equation in a general form.
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ABSTRACT This paper deals with the design of ripple-free deadbeat controllers with performance or performance robustness optimized over controllers within a prescribed settling time. The performance objective of interest is the... more
ABSTRACT This paper deals with the design of ripple-free deadbeat controllers with performance or performance robustness optimized over controllers within a prescribed settling time. The performance objective of interest is the minimization of the maximum absolute tracking error. This leads to consider linfinity optimization problems. On the contrary, the optimization of the performance robustness leads to consider l1 optimization problems. An example is provided to illustrate the results.
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There have been several constructions for the topological degree (or fixed point in-dex) for acyclic type multivalued maps (multimaps) in infinite-dimensional spaces, see for example the works of M. Furi e M. Martelli [6], VV Obukhovski... more
There have been several constructions for the topological degree (or fixed point in-dex) for acyclic type multivalued maps (multimaps) in infinite-dimensional spaces, see for example the works of M. Furi e M. Martelli [6], VV Obukhovski [12], L. Gorniewicz and Z. Kucharski [9] and D. ...
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In this paper, we define a new class of multivalent guiding functions called local multivalent guiding functions and use it to study the global bifurcation problem of periodic soluions to a parameterized differential equation. 2010... more
In this paper, we define a new class of multivalent guiding functions called local multivalent guiding functions and use it to study the global bifurcation problem of periodic soluions to a parameterized differential equation. 2010 Mathematics Subject Classification: 34C23, 34C25
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In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued.... more
In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered. Thereafter, the theory is extended to the case of non-smooth guiding functions.
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The authors describe a method for proving the existence of periodic solutions to n-dimensional systems of the form z ' (t)-Az(t)-Bz(t-τ)=F[z(t)]· The proposed method is based on the harmonic balance method and the theory of... more
The authors describe a method for proving the existence of periodic solutions to n-dimensional systems of the form z ' (t)-Az(t)-Bz(t-τ)=F[z(t)]· The proposed method is based on the harmonic balance method and the theory of reproducing kernels.
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We define a nonoriented coincidence index for a compact, fundamentally restrictible, and condensing multivalued perturbations of a map which is nonlinear Fredholm of nonnegative index on the set of coincidence points. As an application,... more
We define a nonoriented coincidence index for a compact, fundamentally restrictible, and condensing multivalued perturbations of a map which is nonlinear Fredholm of nonnegative index on the set of coincidence points. As an application, we consider an optimal controllability problem for a system governed by a second-order integro-differential equation.
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We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in... more
We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered.
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For an m m -dimensional differential inclusion of the form \[ x ˙ ∈ A ( t ) x ( t ) + F [ t , x ( t ) ] , \dot x \in A(t)x(t) + F[t,x(t)], \] with A A and F F T T -periodic in t t , we prove the existence of a nonconstant periodic... more
For an m m -dimensional differential inclusion of the form \[ x ˙ ∈ A ( t ) x ( t ) + F [ t , x ( t ) ] , \dot x \in A(t)x(t) + F[t,x(t)], \] with A A and F F T T -periodic in t t , we prove the existence of a nonconstant periodic solution. Our hypotheses require m m to be odd, and require F F to have different growth behavior for | x | \left | x \right | small and | x | \left | x \right | large (often the case in applications). The idea is to guarantee that the topological degree associated with the system has different values on two distinct neighborhoods of the origin.
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We consider a nonlocal boundary value problem for a semilinear differential inclusion of a fractional order in a Banach space assuming that its linear part is a non-densely defined HilleYosida operator. We apply the theory of integrated... more
We consider a nonlocal boundary value problem for a semilinear differential inclusion of a fractional order in a Banach space assuming that its linear part is a non-densely defined HilleYosida operator. We apply the theory of integrated semigroups, fractional calculus and the fixed point theory of condensing multivalued maps to obtain a general existence principle (Theorem 3.2). Theorem 3.3 gives an example of a concrete realization of this result. Some important particular cases including a nonlocal Cauchy problem, periodic and anti-periodic boundary value problems are presented.
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In this paper we find existence results for nonlinear variational inequalities involving a multivalued map. Both cases of a lower semicontinuous multimap and an upper semicontinuous one are considered. We solve the problem using a... more
In this paper we find existence results for nonlinear variational inequalities involving a multivalued map. Both cases of a lower semicontinuous multimap and an upper semicontinuous one are considered. We solve the problem using a linearization argument and a suitable continuation principle.
We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic,... more
We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.