Nonexistence of solutions of some inequalities with gradient nonlinearities and fractional Laplacian

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

Nonexistence results for some nonlinear elliptic and parabolic inequalities with functional parameters

We obtain results on nonexistence of nontrivial nonnegative solutions for some elliptic and parabolic inequalities with functional parameters involving the $p(x)$-Laplacian operator. The proof is based on the test function method

On nonexistence of solutions to some nonlinear inequalities with transformed argument

We obtain results on nonexistence of nontrivial solutions for several classes of nonlinear partial differential inequalities and systems of such inequalities with transformed argument

The Management of Coordination of Interests of Stakeholders in Information Security Problems

Запропоновано підхід до застосування теорії ігор як математичного апарату для узгодження інтересів суб’єктів до задач інформаційної безпеки. Подано схему та описано етапи підходу. Детально розглянуто застосування підходу до двох прикладів.This paper proposes an approach to the use of game theory as a mathematical instrument for coordination the interests of stakeholders in the challenges of information security. The scheme and description of the stages for approach are described. The applications of the approach to the two examples are described in detail

Uniqueness of the trivial solution of some inequalities with fractional Laplacian

We obtain sufficient conditions for the uniqueness of the trivial solution for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator

Uniqueness of the trivial solution of some inequalities with fractional Laplacian

We obtain sufficient conditions for the uniqueness of the trivial solution for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator

Blow-up of solutions to some differential equations and inequalities with shifted arguments

Using the test function technique, we obtain sufficient conditions for the blow-up of solutions to some differential equations and inequalities with advanced and delayed arguments, and for systems. Also we obtain upper estimates for the blow-up time

Uniqueness of the trivial solution of some inequalities with fractional Laplacian

We obtain sufficient conditions for the uniqueness of the trivial solution for some classes of nonlinear partial differential inequalities containing the fractional powers of the Laplace operator

Blow-up for nonlinear inequalities with singularities on unbounded sets

Summary: "Many physical phenomena are described by nonlinear equations and inequalities with singular coefficients, for which blow-up situation occurs. In this paper we establish sufficient conditions of blow-up situation for some classes of nonlinear differential inequalities with singularities on unbounded sets.