EIGENVALUE PROBLEMS WITH WEIGHT AND VARIABLE EXPONENT FOR THE LAPLACE OPERATOR
Mihai Mihăilescu, Vicenţiu D. Rădulescu · Analysis and Applications · 2010
This paper deals with an eigenvalue problem for the Laplace operator on a bounded domain with smooth boundary in ℝN(N ≥ 3). We establish that there exist two positive constants λ*and λ* with λ*≤ λ* such that any λ ∈ (0, λ*) is not an eigenvalue of the problem while any λ ∈ [λ*, ∞) is an eigenvalue of the problem.