Concave-convex effects for critical quasilinear elliptic problems

2016/10/14 by C. Goulart, Goulart, C., E. D. da Silva +7 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1610.04652

arxiv created 2016/10/14 · openalex publication_date 2016/10/14 · arxiv updated 2016/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is established existence, multiplicity and asymptotic behavior of positive solutions for a quasilinear elliptic problem driven by the Φ-Laplacian operator. One of these solutions is obtained as ground state solution by applying the well known Nehari method. The semilinear term in the quasilinear equation is a concave-convex function which presents a critical behavior at infinity. The concentration compactness principle is used in order to recover the compactness required in variational methods.

Citations

• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Sign changing solutions for quasilinear superlinear elliptic problems

Cited by

• Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

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