Existence and multiplicity results for a class of p-Laplacian problems with Neumann–Robin boundary conditions

G.A. Afrouzi and M. Khaleghy Moghaddam

Chaos, Solitons & Fractals, 2006, vol. 30, issue 4, 967-973

Abstract: In this paper, we study the following Neumann–Robin boundary value problem-(ϕp(u′(x)))′=λf(u(x)),x∈(0,1),u′(0)=0,u′(1)+αu(1)=0,whereα∈R, λ>0 are parameters and p>1, and p′=pp-1 is the conjugate exponent of p and ϕp(x):=∣x∣p−2x for all x∈R where (ϕp(u′))′ is the one dimensional p-Laplacian and f∈C2[0,∞) such that f(0)<0, or f(0)>0, and also f is increasing and concave up. We shall investigate the existence and multiplicity of nonnegative solutions. Note that in this paper, we shall establish our existence results by using the quadrature method.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:30:y:2006:i:4:p:967-973

DOI: 10.1016/j.chaos.2005.08.172

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