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Publicly Available Published by De Gruyter March 10, 2016

Pairs of Nodal Solutions for a Class of Nonlinear Problems with One-sided Growth Conditions

Alberto Boscaggin and Fabio Zanolin

Abstract

Boundary value problems of Sturm-Liouville and periodic type for the second order nonlinear ODE uʺ + λf(t, u) = 0 are considered. Multiplicity results are obtained, for λ positive and large, under suitable growth restrictions on f(t, u) of superlinear type at u = 0 and of sublinear type at u = ∞. Only one-sided growth conditions are required. Applications are given to the equation uʺ + λq(t)f(u) = 0, allowing also a weight function q(t) of nonconstant sign.

Published Online: 2016-03-10
Published in Print: 2013-02-01

© 2016 by Advanced Nonlinear Studies, Inc.

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