Multiple solutions for elliptic systems with nonlinearities of arbitrary growth

We prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth. Moreover, if the symmetry of the problem is broken by a small enough perturbation term, we find at least three solutions. The proofs utilise a variational setting given by de Figueiredo and Ruf in order to prove an existence's result and the “algebraic” approach based on the Pohozaev's fibering method.     

Soliton solutions for quasilinear Schrödinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].     

Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index

In this paper we study a quasilinear elliptic problem with the Dirichlet boundary condition in a bounded domain involving the operator Au=−Δ_pu−Δ_qu. Assuming that the nonlinearity has a concave-convex behavior we obtain some multiplicity results. More precisely, we obtain five nontrivial solutions; two by a minimization argument, two by the mountain pass theorem, and the other by a cohomological linking theorem.     

An existence theorem for weak solutions for a class of elliptic partial differential systems in Orlicz spaces

We prove the existence of a weak solution of the Dirichlet problem for a class of elliptic partial differential systems in separable Orlicz–Sobolev spaces.     

Existence of multiple solutions for quasilinear systems via fibering method

By using the fibering method introduced by Pohozaev, we prove existence of multiple solutions for a Diriclhlet problem associated to a quasilinear system involving a pair of (p,q)-Laplacian operators.     

Quasilinear elliptic system with coupling on nonhomogeneous critical term

We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. A version of the Concentration-Compactness Principle for this class of systems allows us to verify that the Palais–Smale condition is satisfied below a certain level.     

Sign-changing solutions of critical growth nonlinear elliptic systems

In this paper, we are concerned with the existence of sign-changing solutions of a class of nonlinear elliptic systems with critical growth.     

Structure of least-energy solutions for quasilinear elliptic equations on convex domains

In this paper we study the existence and structure of the least-energy solutions for a class of singularly perturbed quasilinear elliptic equations. Using the moving plane method and a geometric lemma we show that any least-energy solution develops to a single spike-layer solution on convex domains.     

Multiple positive solutions for a quasilinear elliptic equation with critical exponential nonlinearity

Let Ω be a bounded domain in R^N,N≥2, with C² boundary. In this work, we study the existence of multiple positive solutions of the following problem:

     

Multiple solutions of nonlinear elliptic systems

We proved a multiplicity result for a nonlinear elliptic system in R^N. The functional related to the system is strongly indefinite. We investigated the relation between the number of solutions and the topology of the set of the global maxima of the coefficients.     

Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth

This paper is concerned with the positive solutions for generalized quasilinear Schrödinger equations in R^N${\mathbb{R}}^N$ with critical growth which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By using a change of variables and variational argument, we obtain the existence of positive solutions for the given problem.     

Multiplicity for strongly indefinite semilinear elliptic system

In this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system

     

Existence of solutions for a class of singular quasilinear elliptic resonance problems

The paper concerns a resonance problem for a class of singular quasilinear elliptic equations in weighted Sobolev spaces. The equation set studied is one of the most useful sets of Navier-Stokes equations; these describe the motion of viscous fluid substances such as liquids, gases and so on. By using Galerkin-type techniques, the Brouwer fixed point theorem, and a new weighted compact Sobolev-type embedding theorem established by Shapiro, we show the existence of a nontrivial solution.     

Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups

In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.     

On a new class of elliptic systems with nonlinearities of arbitrary growth

We guarantee the existence of infinitely many different pairs of solutions to the system

     

Multiple solutions for a class of biharmonic elliptic systems with Sobolev critical exponent

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems.