Existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems

Existence and Multiplicity of Solutions for Superquadratic Noncooperative Variational Elliptic Systems

(ES)  −∆u = αu− δv + Fu(u, v) in Ω, ∆v = −δu− γv + Fv(u, v) in Ω, u = v = 0 on ∂Ω, where Ω is a bounded open domain in R with smooth boundary, α ≥ 0, δ ≥ 0, γ ≥ 0 are three real parameters and F ∈ C(R,R). The solutions of (ES) represent the steady state solutions of reaction-diffusion systems which are derivedfrom several applications, such as mathematical biology or chemical reactions (see...

Existence and multiplicity of solutions for asymptotically linear nonperiodic Hamiltonian elliptic system

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t This paper is concerned with the following nonperiodic Hamiltonian elliptic system    −u + V and multipli...

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.

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...