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| EXISTENCE, MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS |
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Citation： |
MA Li,SU Ning.EXISTENCE, MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS[J].Chinese Annals of Mathematics B,2004,25(2):275~286 |
| Page view： 1142
Net amount： 819 |
Authors： |
MA Li; SU Ning |
Foundation： |
Project supported by the 973 Project of the Ministry of Science and Technology of China
(No.G1999075107) and a Scientific Grant of Tsinghua University. |
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| Abstract： |
This paper studies the existence of positive solutions of the
Dirichlet problem for the nonlinear equation involving
$p$-Laplacian operator: $-\Delta _pu={{\lambda}}f(u)$ on a bounded
smooth domain $\Omega $ in $\mathbb R^n$. The authors extend part
of the Crandall-Rabinowitz bifurcation theory to this problem.
Typical examples are checked in detail and multiplicity of the
solutions are illustrated. Then the stability for the associated
parabolic equation is considered and a Fujita-type result is
presented. |
Keywords： |
p-Laplacian operator, Bifurcation, Multiplicity, Positive solutions |
Classification： |
35J60, 35K55, 35B32, 35B40, 92D25 |
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