We prove the absence of positive solutions for some semilinear elliptic partial differential ineq... more We prove the absence of positive solutions for some semilinear elliptic partial differential inequalities with transformations of the argument in a half-space. The proofs are based on the test functions method.
Contemporary Mathematics. Fundamental Directions, 2021
In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient condition... more In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient conditions for the absence of nontrivial weak solutions to nonlinear inequalities and systems with integer powers of|the Laplace operator and with a nonlinear term of the form a(x)|(mu)|q+ b(x)|u|s. We obtainoptimal a priori estimates by applying the nonlinear capacity method with an appropriate choice of testfunctions. As a result, we prove the absence of nontrivial weak solutions to nonlinear inequalities and systems by contradiction.
We establish conditions for the blow-up of solutions to several systems of nonlinear differential... more We establish conditions for the blow-up of solutions to several systems of nonlinear differential inequalities, with singularities on unbounded sets.
We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequ... more We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequalities and systems containing the p-Laplace operators and coefficients possessing singularities on the boundary.
summary:We obtain sufficient conditions for nonexistence of nontrivial solutions for some classes... more summary:We obtain sufficient conditions for nonexistence of nontrivial solutions for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator
We consider the existence problem for local (with respect to time) solutions of quasilinear evolu... more We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.
We analyze the problem of blow-up of global solutions of a semilinear wave equation with a potent... more We analyze the problem of blow-up of global solutions of a semilinear wave equation with a potential and with a possible degeneration at infinity for nonnegative initial data with compact support. By using the nonlinear capacity method, we prove the theorem on the nonexistence of such a solution for a subcritical and the critical nonlinearity exponent.
Using a modification of the nonlinear capacity method, we establish sufficient conditions of blow... more Using a modification of the nonlinear capacity method, we establish sufficient conditions of blow-up of solutions for a generalized heat inequality with possibly degenerate coefficients from the Caratheodory class and upper estimates of the blow-up time.
We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequ... more We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequalities and systems containing the p-Laplace operators and coefficients possessing singularities on the boundary.
We establish conditions for the blow-up of solutions to several systems of nonlinear differential... more We establish conditions for the blow-up of solutions to several systems of nonlinear differential inequalities, with singularities on unbounded sets.
Summary. - We obtain nonexistence results for systems of stationary and evolutional partial diffe... more Summary. - We obtain nonexistence results for systems of stationary and evolutional partial differential inequalities that involve p-Laplacian and similar nonlinear operators as well as gradient nonlinearities. Our proofs are based on the nonlinear capacity method.
We prove the absence of positive solutions for some semilinear elliptic partial differential ineq... more We prove the absence of positive solutions for some semilinear elliptic partial differential inequalities with transformations of the argument in a half-space. The proofs are based on the test functions method.
Contemporary Mathematics. Fundamental Directions, 2021
In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient condition... more In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient conditions for the absence of nontrivial weak solutions to nonlinear inequalities and systems with integer powers of|the Laplace operator and with a nonlinear term of the form a(x)|(mu)|q+ b(x)|u|s. We obtainoptimal a priori estimates by applying the nonlinear capacity method with an appropriate choice of testfunctions. As a result, we prove the absence of nontrivial weak solutions to nonlinear inequalities and systems by contradiction.
We establish conditions for the blow-up of solutions to several systems of nonlinear differential... more We establish conditions for the blow-up of solutions to several systems of nonlinear differential inequalities, with singularities on unbounded sets.
We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequ... more We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequalities and systems containing the p-Laplace operators and coefficients possessing singularities on the boundary.
summary:We obtain sufficient conditions for nonexistence of nontrivial solutions for some classes... more summary:We obtain sufficient conditions for nonexistence of nontrivial solutions for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator
We consider the existence problem for local (with respect to time) solutions of quasilinear evolu... more We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.
We analyze the problem of blow-up of global solutions of a semilinear wave equation with a potent... more We analyze the problem of blow-up of global solutions of a semilinear wave equation with a potential and with a possible degeneration at infinity for nonnegative initial data with compact support. By using the nonlinear capacity method, we prove the theorem on the nonexistence of such a solution for a subcritical and the critical nonlinearity exponent.
Using a modification of the nonlinear capacity method, we establish sufficient conditions of blow... more Using a modification of the nonlinear capacity method, we establish sufficient conditions of blow-up of solutions for a generalized heat inequality with possibly degenerate coefficients from the Caratheodory class and upper estimates of the blow-up time.
We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequ... more We obtain sufficient conditions for the nonexistence of positive solutions to some elliptic inequalities and systems containing the p-Laplace operators and coefficients possessing singularities on the boundary.
We establish conditions for the blow-up of solutions to several systems of nonlinear differential... more We establish conditions for the blow-up of solutions to several systems of nonlinear differential inequalities, with singularities on unbounded sets.
Summary. - We obtain nonexistence results for systems of stationary and evolutional partial diffe... more Summary. - We obtain nonexistence results for systems of stationary and evolutional partial differential inequalities that involve p-Laplacian and similar nonlinear operators as well as gradient nonlinearities. Our proofs are based on the nonlinear capacity method.
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Papers by Evgeny Galakhov