Compact embeddings and indefinite semilinear elliptic problems

Compact Embeddings and Indefinite Semilinear Elliptic Problems

Our purpose is to find positive solutions u ∈ D(R ) of the semilinear elliptic problem −∆u = h(x)u for 2 < p. The function h may have an indefinite sign. Key ingredients are a h-dependent concentration-compactness Lemma and a characterization of compact embeddings of D(R ) into weighted Lebesgue spaces.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Asymmetric Elliptic Problems with Indefinite Weights

– We prove the existence of a first nontrivial eigenvalue for an asymmetric elliptic problem with weights involving the laplacian (cf. (1.2) below) or more generally the p-laplacian (cf. (1.3) below). A first application is given to the description of the beginning of the Fučik spectrum with weights for these operators. Another application concerns the study of nonresonance for the problems (1....

Complexity of Indefinite Elliptic Problems By Arthur

This paper deals with the approximate solution of a linear regularly-elliptic 2mth-order boundary-value problem Lu = f, with / 6 Hr(Q) for r > —m. Suppose that the problem is indefinite, i.e., the variational form of the problem involves a weaklycoercive bilinear form. Of particular interest is the quality of the finite element method (FEM) of degree k using n inner products of /. The error of ...