Multiplicity Results for Classes of One-dimensional p-Laplacian Boundary-value Problems with Cubic-like Nonlinearities
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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.
CitationAddou, I. (2000). Multiplicity results for classes of one-dimensional p-Laplacian boundary-value problems with cubic-like nonlinearities. Electronic Journal of Differential Equations, 2000(52), pp. 1-42.
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