Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 323-334

Perturbations near resonance for the p-Laplacian in N

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

Received 10 September 2001

Copyright © 2002 To Fu Ma and Maurício Luciano Pelicer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a multiplicity result for the perturbed p-Laplacian equation Δpuλg(x)|u|p2u=f(x,u)+h(x)inN, where 1<p<N and λ is near λ1, the principal eigenvalue of the weighted eigenvalue problem Δpu=λg(x)|u|p2u in N. Depending on which side λ is from λ1, 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.