Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.
Existence of positive solutions for quasilinear elliptic systems involving the -Laplacian.
Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems.
Existence of solutions for a class of elliptic systems in involving the p-Laplacian.
Existence of solutions for a class of elliptic systems in involving the -Laplacian.
Existence of solutions for a semilinear elliptic system
This paper deals with the existence of solutions to the following system:−Δu+u=αα+βa(x)|v|β|u|α−2u inRN−Δv+v=βα+βa(x)|u|α|v|β−2v inRN. With the help of the Nehari manifold and the linking theorem, we prove the existence of at least two nontrivial solutions. One of them is positive. Our main tools are the concentration-compactness principle and the Ekeland’s variational principle.
Existence of solutions for elliptic systems involving operators in divergence form.
Existence of solutions for elliptic systems with nonlocal terms in one dimension.
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.
Existence results for a fourth order partial differential equation arising in condensed matter physics
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem...
Existence results for elliptic systems involving critical Sobolev exponents.
Existence results for strongly indefinite elliptic systems.
Existences and boundary behavior of boundary blow-up solutions to quasilinear elliptic systems with singular weights.
Exterior problem of the Darwin model and its numerical computation
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
Exterior problem of the Darwin model and its numerical computation
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell's equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
Formes harmoniques et cohomologie relative des algèbres de Lie
Full -regularity for minimizers of integral functionals with -growth.
Fundamental inequalities on firmly stratified sets and some applications.
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.