Existence and Multiplicity of Solutions for p-Laplacian Neumann Problems
- 64 Downloads
In this paper, existence theorems are proved for p-Laplacian Neumann problems under the Landesman–Lazer type condition. Our results are derived from a classical saddle point theorem and the least action principle respectively. Furthermore, multiplicity of solutions is established by applying a known multiple critical points result due to H. Brezis and L. Nirenberg. The above-mentioned conclusions are based on variational methods.
KeywordsNeumann problem p-Laplacian critical point saddle point theorem Landesman–Lazer type condition
Mathematics Subject Classification35J50 49J35
- 17.Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. In: CBMS Regional Conference Series in Mathematics, 65. Published for the Conference Board of the Mathematical Sciences, Washington, DC. American Mathematical Society, Providence (1986)Google Scholar