Multiplicity Results for Classes of One-dimensional p-Laplacian Boundary-value Problems with Cubic-like Nonlinearities
Date
2000-07-03
Authors
Addou, Idris
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study boundary-value problems of the type
-(φp(u'))' = λƒ(u), in (0, 1)
u(0) = u(1) = 0,
where p > 1, φp(x) = |x|p-2 x, and λ > 0. We provide multiplicity results when ƒ behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter q > 1. We shall show hos changes in the position of q with respect to p lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that ƒ is half-odd; a condition generalizing the usual oddness. We use a quadrature method.
Description
Keywords
p-Laplacian, Time-maps, Multiplicity results, Cubic-like nonlinearities
Citation
Addou, I. (2000). Multiplicity results for classes of one-dimensional p-Laplacian boundary-value problems with cubic-like nonlinearities. <i>Electronic Journal of Differential Equations, 2000</i>(52), pp. 1-42.
Rights
Attribution 4.0 International