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

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  • Afrouzi, G.A.
  • Moghaddam, M. Khaleghy

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.

Suggested Citation

  • Afrouzi, G.A. & Moghaddam, M. Khaleghy, 2006. "Existence and multiplicity results for a class of p-Laplacian problems with Neumann–Robin boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 967-973.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:4:p:967-973
    DOI: 10.1016/j.chaos.2005.08.172
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