Existence of two solutions for singular Φ-Laplacian problems

2022/06/30 by Pasquale Candito, Candito, Pasquale, Umberto Guarnotta +3
Engineering · Mathematics · #35J20 #35J25 #35J62 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.15061

openalex publication_date 2022/06/30 · openalex created_date 2022/07/03 · openalex updated_date 2026/07/28

Abstract

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the Φ-Laplacian operator and the reaction term can be non-monotone. The main tools employed are a local minimum theorem and the Mountain Pass theorem, together with the truncation technique. Global C^1,τ regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.

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