Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions

In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.

DETERMINATION OF ELASTIC DEFORMATION OF SPRING DEFLECTION OF THE SEALING UNIT

The article discusses the definition of elastic deformation - deflection of the spring of the sealing unit of the Christmas tree valve. Using variational methods, the optimal solution of the spring deflection of the gate valve sealing unit was determined. It is proved that the obtained formulas give rather accurate results of the spring deflection of the valve sealing unit.

Nonpotentiality of a diffusion system and the construction of a semi-bounded functional

The wide prevalence and the systematic variational principles are used in mathematics and applications due to a series of remarkable consequences among which the possibility to establish the existence of the solutions of the initial equations, and the determination of stable approximations of the solutions of the considered equations by the so-called variational methods. In this connection, it is natural for a given system of equations to investigate the problem of the existence of its variational formulations. It can be considered as the inverse problem of the calculus of variations. The main goal of this work is to study this problem for a diffusion system of partial differential equations. A key object is the criterion of potentiality. On its ground, the nonpotentiality of the operator of the given boundary value problem with respect to the classical bilinear form is proved. This system does not admit a matrix variational multiplier of the given form. Thus, the diffusion system cannot be deduced from the classical Hamilton’s principle. We posed the question that whether there exists a functional semi-bounded on solutions to the boundary value problem. We have done the algorithm of the constructive determination of such a functional. The main value of constructed functional action will be in applications of direct variational methods.

Existence and multiplicity of solutions for Kirchhoff–Schrödinger–Poisson system with critical growth

This paper is concerned with the following Kirchhoff–Schrödinger–Poisson system: [Formula: see text] where constants [Formula: see text], [Formula: see text] and [Formula: see text] are the parameters. Under some appropriate assumptions on [Formula: see text], [Formula: see text] and [Formula: see text], we prove the existence and multiplicity of nontrivial solutions for the above system via variational methods. Some recent results from the literature are greatly improved and extended.

Multiplicity of solutions for Robin problem involving the p(x)-laplacian

This paper is concerned with the existence and multiplicity of solutions for p(x)-Laplacian equations with Robin boundary condition. Our technical approach is based on variational methods.

On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions

In this article, we study the existence of solutions for nonlocal p x -biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.