On a variational approximation method for a class of elliptic Eigenvalue problems in composite structures

An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures

— We consider a second-order elliptic eigenvalue problem on a convex polygonal domain, divided in M non-overlapping subdomains. The conormal derivative of the unknown function is continuons on the interfaces, while the function itself is discontinuons. In this paper, we study the finite element approximation without and with numerical quadrature of this eigenvalue problem by means of the pertur...

A numerical technique for solving a class of 2D variational problems using Legendre spectral method

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems