Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Abstract

The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space R N . The solutions will be obtained in a subspace of the Sobolev space W 1,p (R N ). The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle.

A MULTIPLICITY RESULT FOR A CLASS OF EQUATIONS OFp-LAPLACIAN TYPE WITH SIGN-CHANGING NONLINEARITIES

“…It should be observed that the above examples have not been considered in [2,8,10] yet. For more information and connection on these operators, the reader may consult either [2] or [8] and the references therein.…”

“…For more information and connection on these operators, the reader may consult either [2] or [8] and the references therein.…”

“…x ∈ , p 2 and λ > 0 is a parameter. When h 0 and h 1 belong to L ∞ ( ), the problem has been studied by many authors (see [2,8,10] for details). Here we study the situation that h 0 ∈ L p p−1 ( ) and h 1 ∈ L 1 loc ( ).…”

On the Existence of Weak Solutions for a Degenerate and Singular Elliptic System in ℝ N

“…Now, dividing the above inequality by u h,a,b and passing to the limit we obtain a con- We follow the method as those used in [11]. By Remark 1.2, the embeddings…”

Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain

“…The p-Laplacian operator Δ p u = − div |∇u| p−2 ∇u is a special case of the operator − div a(x, ∇u) . We refer the readers to some recent works [8,12,13] on elliptic problems of p-Laplacian type in the general case.…”