Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 323-334
doi:10.1155/S1085337502203073
Perturbations near resonance for the p-Laplacian in ℝN
To Fu Ma1
and Maurício Luciano Pelicer2
1Departamento de Matemática, Universidade Estadual de Maringá, Maringá 87020-900, PR, Brazil
2Departamento de Ciências, Universidade Estadual de Maringá, Goioerê 87360-000, PR, Brazil
Abstract
We study a multiplicity result for the perturbed p-Laplacian equation −Δpu−λg(x)|u|p−2u=f(x,u)+h(x) in ℝN, where 1<p<N and λ is near λ 1, the principal eigenvalue of the weighted eigenvalue problem −Δpu=λg(x)|u|p−2u in ℝN. Depending on which side λ is from λ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.