Abstract
Via the linking theorem, the existence of nontrivial solutions for a nonlinear elliptic Dirichlet boundary value problem with an inverse square potential is proved.
Highlights
This paper is concerned with the existence of nontrivial solutions to the following problem:
We mention that when p = 2∗, the existence of nontrivial solutions of (1.1) has been proved in [2, Theorem 1.3]
If 0 ≤ μ < μ, problem (1.3) has a positive solution for 0 < λ < λ1, where λ1 denotes the first eigenvalue of the operator − − μ/|x|2
Summary
This paper is concerned with the existence of nontrivial solutions to the following problem:. Where 0 ∈ Ω ⊂ RN (N ≥ 3) is a bounded domain with smooth boundary, 0 ≤ μ < μ = ((N − 2)/2), and μ is the best constant in the Hardy inequality: C. (cf [3, Lemma 2.1]), 2 < p < 2∗, where 2∗ = 2N/(N − 2) is the so-called critical Sobolev exponent and λ > 0 is a parameter. In Theorem 1.3 we prove, for small λ > 0, the existence of a solution to u p−1.
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