A complement to the Fredholm theory of elliptic systems on bounded domains.
A maximum principle for systems with variational structure and an application to standing waves
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.
A predator-prey model with combined death and competition terms
The existence of a positive solution for the generalized predator-prey model for two species are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.
Asymptotic behavior of ground state solution for Hénon type systems.
Existence of entire positive solutions for a class of semilinear elliptic systems.
Existence of entire solutions for semilinear elliptic systems under the Keller-Osserman condition.
Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.
Existence of nonnegative solutions to positone-type problems in with indefinite weights.
Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems.
Existence of solutions for a class of elliptic systems in involving the -Laplacian.
Existence of solutions for a system of elliptic partial differential equations.
Existence of solutions for elliptic systems with nonlocal terms in one dimension.
Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.
Existence of weak solutions for a nonlinear elliptic system.
Existence result for a class of elliptic systems with indefinite weights in .
Existence result for a class of nonlinear elliptic systems on punctured unbounded domains.
Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth
For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle.
Infinitely many periodic solutions for variable exponent systems.
Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems
This paper is concerned with the following periodic Hamiltonian elliptic system Assuming the potential V is periodic and 0 lies in a gap of , is periodic in x and asymptotically quadratic in , existence and multiplicity of solutions are obtained via variational approach.
Infinitely many solutions of strongly indefinite semilinear elliptic systems.