On an indefinite semilinear elliptic problem on RN

On a singular nonlinear semilinear elliptic problem

where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under variou...

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.

Existence of Positive Entire Solutions of Semilinear Elliptic Equations on Rn

has been studied by several authors, where 1 < p for N = 2, 1 < p < (N + 2)/(N − 2) for N ≥ 3 and Q(x) is a positive bounded continuous function. If Q(x) is a radial function, we can find infinity many solutions of problem (PQ) by restricting our attention to the radial functions (cf. [2, 5]). IfQ(x) is nonradial, we encounter a difficulty caused by the lack of a compact embedding of Sobolev ty...

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

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems