Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 323-334
Perturbations near resonance for the -Laplacian in
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 -Laplacian equation , where and is near , the principal eigenvalue of the weighted eigenvalue problem in . Depending on which side is from , 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.