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Aug 26, 2023 · In this paper, a class of nonlinear fractional differential equations with periodic boundary condition is investigated. Although the nonlinearity of the equation and the Green's function are sign-changing, the results of the existence and nonexistence of positive solutions are obtained by using the Schaefer's ...
Aug 15, 2023 · The paper is organized as follows: in Section 2 we deduce the optimizers of (CKN) inequality and give the uniqueness of positive radial solutions of equation (1.15). Section 3 is devoted to characterizing all solutions to the linearized equation (1.16) for Sobolev critical case. In Section 4, we study the remainder ...
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Jan 15, 2024 · In this paper, we consider a boundary control problem associated with a fourth order parabolic type equation in a bounded two-dimensional domain. The solution with the control function on the border of the considered domain is given. The constraints on the control are determined to ensure that the average value of ...
May 22, 2024 · In this article, we study a class of nonlinear fractional differential equations with mixedtype boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction ...
Oct 23, 2023 · Positive solutions and nonlinear eigenvalue problems for functional differential equations. J Henderson, W Yin. Applied mathematics letters 12 (2), 63-68, 1999. 26, 1999. Existence of solutions for fourth order boundary value problems on a time scale ... Uniqueness implies existence for three-point boundary value ...
Nov 12, 2023 · Abstract. This paper is dedicated to investigating the Lp-bounds of wave operators W±(H, ∆2) associated with fourth-order Schrödinger operators H = ∆2 + V on R3. We consider that real potentials satisfy |V (x)| % 〈x〉−µ for some µ > 0. A recent work by Goldberg and Green [22] has.
May 30, 2024 · The Sturm--Liouville problem asks to find nontrivial (not identically zero) solutions, called eigenfunctions and corresponding values of parameter λ, called eigenvalues. A Sturm--Liouville problem is called singular if either the coefficient p(x) vanishes at least at one end point x = 𝑎 or/and x ...
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Apr 4, 2024 · Abstract: A method is described to solve the time-dependent incompressible Navier-Stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions. The scheme is fourth-order accurate in space and uses the momentum equations for the velocity coupled to a Poisson equation ...
Jan 15, 2024 · This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization ...
Dec 4, 2023 · [PDF 316KB] (156). SPECTRAL-GALERKIN APPROXIMATION BASED ON REDUCED ORDER SCHEME FOR FOURTH ORDER EQUATION AND ITS EIGENVALUE PROBLEM WITH SIMPLY SUPPORTED PLATE BOUNDARY CONDITIONS ... GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR FIRST-ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS WITH INDEFINITE WEIGHT. Xiaoxiao Su, ...
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