On a superquadratic elliptic system with strongly indefinite structure

Multiplicity for Symmetric Indefinite Functionals: Application to Hamiltonian and Elliptic Systems

In this article we study the existence of critical points for certain superquadratic strongly indefinite even functionals appearing in the study of periodic solutions of Hamiltonian systems and solutions of certain class of Elliptic Systems. We first present two abstract critical point theorems for even functionals. These results are well suited for our applications, but they are interesting by...

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...

Critical Point Theory Applied to a Class of the Systems of the Superquadratic Wave Equations

We show the existence of a nontrivial solution for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary conditions and periodic conditions with a superquadratic nonlinear terms at infinity which have continuous derivatives. We approach the variational method and use the critical point theory which is the Linking Theorem for the strongly indefinite corres...

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

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...