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| Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition |
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Citation： |
Zifei SHEN,Chenyin QIAN.Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition[J].Chinese Annals of Mathematics B,2009,30(4):397~412 |
| Page view： 1831
Net amount： 1902 |
Authors： |
Zifei SHEN; Chenyin QIAN; |
Foundation： |
by the National Natural Science Foundation of China (No. 10771141) and the Zhejiang
Provincial Natural Science Foundation of China (No. Y7080008). |
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| Abstract： |
The authors study the $p(x)$-Laplacian equations with nonlinear
boundary condition. By using the variational method, under
appropriate assumptions on the perturbation terms $f_1(x,u)$,
$f_2(x,u)$ and $h_1(x)$, $h_2(x)$, such that the associated
functional satisfies the ``mountain pass lemma'' and ``fountain
theorem'' respectively, the existence and multiplicity of solutions
are obtained. The discussion is based on the theory of variable
exponent Lebesgue and Sobolev spaces. |
Keywords： |
p(x)-Laplacian, Nonlinear boundary condition, (PS) condition, Mountain
pass lemma, Fountain theorem |
Classification： |
35J20, 35J25 |
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