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1997 On the existence and multiplicity of positive solutions of the $p$-Laplacian separated boundary value problem
A. K. Ben-Naoum, C. De Coster
Differential Integral Equations 10(6): 1093-1112 (1997).

Abstract

Using the lower and upper solutions method together with degree theory, we study the existence and multiplicity of positive solutions for the problem $$ (\varphi_{p}(u'))'+f(t,u)=0,\ \ a_{1}\varphi_{p}(u(a))-a_{2} \varphi_{p}(u'(a))=0,\ b_{1}\varphi_{p}(u(b))+b_{2} \varphi_{p}(u'(b))=0, $$ where $\varphi_{p} (s):=|s|^{p-2}s, \,p>1$, $a_1,b_1\in\Bbb R$, $a_2,b_2\in\Bbb R^+$, $a_1^2+a_2^2>0$, $b_1^2+b_2^2>0.$ The function $f$ satisfies assumptions related to the classically called sublinear, superlinear, subsuperlinear, or supersublinear cases. Our results improve the recent ones of L.H. Erbe-H. Wang ([21]) and L.H. Erbe-S. Hu-H. Wang ([20]).

Citation

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A. K. Ben-Naoum. C. De Coster. "On the existence and multiplicity of positive solutions of the $p$-Laplacian separated boundary value problem." Differential Integral Equations 10 (6) 1093 - 1112, 1997.

Information

Published: 1997
First available in Project Euclid: 1 May 2013

zbMATH: 0940.35086
MathSciNet: MR1608037

Subjects:
Primary: 35J65
Secondary: 34B15, 35B32

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 6 • 1997
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