2015/08/26 by M. J. Alves, Maria José De Castro Alves, Ronaldo B. Assunção +6
Computer Science · Mathematics · #35B09 #35B38 #35B45 (Secondary) #35J10 #35J20 #35J92 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Applied mathematics #Class (philosophy) #Compact space #Computer science #Energy functional #FOS: Mathematics #Infinity #Laplace operator #Lemma (botany) #Mathematical analysis #Mathematics #Mountain pass #Nonlinear Partial Differential Equations #Nonlinear system #Numerical methods in inverse problems #Operator (biology) #Order (exchange) #Physics #Pure mathematics #math.AP #msc:35B09 #msc:35B38 #msc:35B45 #msc:35J10 #msc:35J20 #msc:35J92 #p-Laplacian
paper · pdf · doi:10.48550/arxiv.1508.06447
22 pages
arxiv created 2015/08/26 · openalex publication_date 2015/08/26 · arxiv updated 2015/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The main purpose of this paper is to establish the existence of positive solutions to a class of quasilinear elliptic equations involving the (p-q)-Laplacian operator. We consider a nonlinearity that can be subcritical at infinity and supercritical at the origin; we also consider potential functions that can vanish at infinity. The approach is based on variational arguments dealing with the mountain-pass lemma and an adaptation of the penalization method. In order to overcome the lack of compactness we modify the original problem and the associated energy functional. Finally, to show that the solution of the modified problem is also a solution of the original problem we use an estimate obtained by the Moser iteration scheme.