Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Multi-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions

In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generaliz...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

New conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

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.