Topological results on a certain class of functionals and application

@article{Bahri1981TopologicalRO,
title={Topological results on a certain class of functionals and application},
author={A. Bahri},
journal={Journal of Functional Analysis},
year={1981},
volume={41},
pages={397-427}
}

We study in this paper problems of the type Δu + ¦u¦p − 1 u = ƒ(x), Ω bounded ⊂ RN, u = 0¦∂Ω, (I) where ƒ(x) is given and where p ϵ (1, (N + 2N − 2)) (p ϵ (1, + ∞) if N ⩽ 2). Our main result is that (I) has an infinite number of solutions for a residual set of ƒ in H−1 (Ω). In particular, for many n ∈ N there exists an open and dense subset of ƒ in H−1(Ω) such that (I) has n distinct solutions for such an ƒ This result is to be related to the conjecture developed in [1] of the existence of an… CONTINUE READING