Multiplicity of solutions for resonant and non-resonant asymptotically linear elliptic problems

2017/08/10 by J. R. Nascimento, Nascimento, José R. S., Marcos T. O. Pimenta +3
Computer Science · Mathematics · #35J15 #35J25 #35J61 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1708.03399

openalex publication_date 2017/08/10 · openalex created_date 2017/08/31 · openalex updated_date 2026/07/28

Abstract

Results about existence of a signed ground state solution and multiple solutions (if f is odd with respect to the second variable) are proven for a class of asymptotically linear elliptic problems involving a Carathéodory type nonlinearity satisfying assumptions weaker than (fF) in \citeGLZ or (F₂)₊ in \citeCM. A close relation between the behaviour of lim_{|t|→ ∞}f(x, t)/|t| and the number of solutions is stablished.

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