Pairs of nontrivial solutions to concave-linear-convex type elliptic\n problems

2019/12/11 by Pasquale Candito, Candito, Pasquale, S. Marano +3
Mathematics · #35J20 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J25 #Secondary 35B33

paper · pdf · doi:10.48550/arxiv.1912.05648

openalex publication_date 2019/12/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We obtain a pair of nontrivial solutions for a class of concave-linear-convex\ntype elliptic problems that are either critical or subcritical. The solutions\nwe find are neither local minimizers nor of mountain pass type in general. They\nare higher critical points in the sense that they each have a higher critical\ngroup that is nontrivial. This fact is crucial for showing that our solutions\nare nontrivial. We also prove some intermediate results of independent interest\non the localization and homotopy invariance of critical groups of functionals\ninvolving critical Sobolev exponents.\n

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