2013/10/22 by Marcos L. M. Carvalho, M. L. Carvalho, J. V. Goncalves +5
Computer Science · Mathematics · #35B45 #35J60 #35J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:35B45 #msc:35J60 #msc:35J65
paper · pdf · doi:10.48550/arxiv.1310.5903
21 pages
arxiv created 2013/10/22 · openalex publication_date 2013/10/22 · arxiv updated 2013/10/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In 2009 Loc and Schmitt established a result on sufficient conditions for multiplicity of solutions of a class of nonlinear eignvalue problems for the p-Laplace operator under Dirichlet boundary conditions, extending an earlier result of 1981 by Peter Hess for the Laplacian. Results on necessary conditions for existence were also established. In the present paper the authors extend the main results by Loc and Schmitt to the Φ-Laplacian. To overcome the difficulties with this much more general operator it was necessary to employ regularity results by Lieberman, a strong maximum principle by Pucci and Serrin and a general result on lower and upper solutions by Le.