A Seven-Positive-Solutions Theorem for a Superlinear Problem
- 1 May 2004
- journal article
- Published by Walter de Gruyter GmbH in Advanced Nonlinear Studies
- Vol. 4 (2) , 149-164
- https://doi.org/10.1515/ans-2004-0202
Abstract
We consider the superlinear boundary value problem uʺ + aμ(t)uγ+1 = 0, u(0) = 0, u(1) = 0, where γ > 0 and aμ(t) is a sign indefinite weight of the form a+(t)−μa−(t). We prove, for μ positive and large, the existence of 2k − 1 positive solutions where k is the number of positive humps of aμ(t) which are separated by k − 1 negative humps. For sake of simplicity, the proof is carried on for the case k = 3 yielding to 7 positive solutions. Our main argument combines a modified shooting method in the phase plane with some properties of the blow up solutions in the intervals where the weight function is negative.Keywords
This publication has 1 reference indexed in Scilit:
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