This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

In this note, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation −∆pu + |u|p−2u = f(x, u) in a smooth bounded domain Ω of RN with nonlinear boundary conditions |∇u|p−2 ∂u ∂ν = g(x, u) on ∂Ω. The proof is based on variational arguments.

In this paper, we investigate the existence of solutions for a class quasilinear elliptic system. By developing Moser iteration technique, obtain that system has nontrivial solution (uλ, vλ) with ‖(uλ, vλ)‖∞ ≤ 2 every λ large enough when nonlinear term F satisfies some growth conditions only in circle center 0 and radius 4, families {(uλ, vλ)} satisfy ‖ → as ∞. Moreover, because interaction u v...

The present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is introduced and the definition of its monotonicity is given. This definition is closely associated with the prope...

We consider, for a bounded open domain Ω in Rn; (n ≥ 1) and function u : → ℝm; (m the quasilinear elliptic system: (QESw)(f,g) (0.1) Which is Dirichlet problem. Here, v belongs to dual space , f g satisfy some stan- dard continuity growth conditions. we will show existence of weak solution this problem four following cases: σ mono- tonic, strictly monotonic, quasi montone derives from convex po...

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form A(u) + g(x, u,∇u) = h, where A is a Leray-Lions operator from W 1,p 0 (Ω, w) to its dual. On the nonlinear term g(x, s, ξ), we assume growth conditions on ξ, not on s, and a sign condition on s.

A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the H and the L norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Application to numerical homogenization methods is considered.

In this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with an operator that is not necessarily bounded. For that, we use the bifurcation theory and obtain the existence of positive solutions for a range of values of the bifurcation parameter.

We study the existence and concentration of positive solutions for the quasilinear elliptic equation −ε2u′′ − ε2(u2)′′u + V (x)u = h(u) in R as ε → 0, where the potential V : R → R has a positive infimum and inf∂Ω V > infΩ V for some bounded domain Ω in R, and h is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.

In the present paper, a quasilinear elliptic problem with a critical Sobolev exponent and a Hardy-type term is considered. By means of a variational method, the existence of nontrivial solutions for the problem is obtained. The result depends crucially on the parameters p, t, s, λ and μ. c © 2007 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33