Linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance without landesman-lazer conditions

2014/10/27 by Alzaki Fadlallah, Fadlallah, Alzaki · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #math.AP

paper · pdf · doi:10.48550/arxiv.1410.7315

openalex publication_date 2014/10/27 · arxiv created 2014/10/28 · arxiv updated 2014/10/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to satisfy Landesman-Lazer conditions or the monotonicity assumption. The nonlinearity may be unbounded. The nonlinearity interact, in some sense with the Steklov spectrum on boundary nonlinearity. The proofs are based on a priori estimates for possible solutions to a homotopy on suitable trace and topological degree arguments.

Cited by

• Linear elliptic system with nonlinear boundary conditions without Landesman-Lazer conditions
• Generalized spectrum of Steklov-Robin problem for elliptic system

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