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2014 Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p-Laplacian
Ruyun Ma, Lingfang Jiang
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/810193

Abstract

We consider the equations involving the one-dimensional p-Laplacian (P): (utp-2u(t))+λf(u(t))=0, 0<t<1, and u(0)=u(1)=0, where p>1,λ>0,fC1(R;R),f(s)s>0, and s0. We show the existence of sign-changing solutions under the assumptions f=lim|s|(fs/sp-1)=+ and f0=lim|s|0(f(s)/sp-1)[0,]. We also show that (P) has exactly one solution having specified nodal properties for λ(0,λ*) for some λ*(0,). Our main results are based on quadrature method.

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Ruyun Ma. Lingfang Jiang. "Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p-Laplacian." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/810193

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131883
MathSciNet: MR3253632
Digital Object Identifier: 10.1155/2014/810193

Rights: Copyright © 2014 Hindawi

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