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The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

Volume 75 / 2000

Bing Liu, Jianshe Yu Annales Polonici Mathematici 75 (2000), 271-280 DOI: 10.4064/ap-75-3-271-280

Abstract

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x'(t), x'(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).

Authors

  • Bing Liu
  • Jianshe Yu

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