Some Results on the 1-Laplacian Elliptic Problems with Singularities and Robin Boundary Conditions

2024/10/26 by Mohamed El Hichami, Hichami, Mohamed El, Youssef El Hadfi +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2410.20028

Abstract

In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \ -Δ_pu_p=\fracfu_p^γ · amp; \hboxin Ω, \frac∂ u_p∂ σ+λ\vert u_p\vert^p-2 u_p+\vert u_p\vert^s-1u_p=\fracgu_p^η · amp; \hboxon ∂Ω, . where Ω⊂ ℝ^m represents an open bounded domain, with smooth boundary, m ≥ 2, the symbol σ stands for the unit outward normal vector, Δ_pu:=div(\vert∇ u\vert^p-2∇ u) is the p-Laplacian operator (1≤ p0 and s≥ 1. The function f∈ L^(m)/(p)(Ω) is a nonnegative additionally λ and g are nonnegative functions in L^∞(∂ Ω).

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