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STRICTLY POSITIVE SOLUTIONS FOR ONE-DIMENSIONAL NONLINEAR PROBLEMS INVOLVING THE $p$-LAPLACIAN

Part of: Elliptic equations and systems Boundary value problems

Published online by Cambridge University Press:  06 September 2013

U. KAUFMANN  and
I. MEDRI
U. KAUFMANN*
Affiliation:
FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina
I. MEDRI
Affiliation:
FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina email medri@mate.uncor.edu
*
✉kaufmann@mate.uncor.edu
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Abstract

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Let $\Omega $ be a bounded open interval, and let $p\gt 1$ and $q\in (0, p- 1)$. Let $m\in {L}^{{p}^{\prime } } (\Omega )$ and $0\leq c\in {L}^{\infty } (\Omega )$. We study the existence of strictly positive solutions for elliptic problems of the form $- (\vert {u}^{\prime } \mathop{\vert }\nolimits ^{p- 2} {u}^{\prime } ){\text{} }^{\prime } + c(x){u}^{p- 1} = m(x){u}^{q} $ in $\Omega $, $u= 0$ on $\partial \Omega $. We mention that our results are new even in the case $c\equiv 0$.

Keywords

elliptic one-dimensional problemsindefinite nonlinearitiesp-Laplacianstrictly positive solutions

MSC classification

Secondary: 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems 35J25: Boundary value problems for second-order elliptic equations 35J61: Semilinear elliptic equations

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 243 - 251
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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