Lin Zhao, Peihao Zhao, Xiaoxia Xie
Abstract:
We establish the existence and multiplicity of weak solutions
of a problem involving a uniformly convex elliptic operator
in divergence form.
We find one nontrivial solution by the mountain pass lemma,
when the nonlinearity has a
-superlinear
growth at infinity,
and two nontrivial solutions by minimization and mountain pass
when the nonlinear term has a
-sublinear
growth at infinity.
Submitted January 1, 2011. Published March 31, 2011.
Math Subject Classifications: 35A15, 35J20, 35J62.
Key Words: Nonlinear elliptic equations; uniformly convex;
mountain pass lemma; three critical points theorem.
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Lin Zhao School of Mathematics and Statistics, Lanzhou University Lanzhou, Gansu 730000, China email: zhjz9332003@gmail.com |
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Peihao Zhao School of Mathematics and Statistics, Lanzhou University Lanzhou, Gansu 730000, China email: zhaoph@lzu.edu.cn |
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Xiaoxia Xie School of Mathematics and Statistics, Lanzhou University Lanzhou, Gansu 730000, China email: xiexx06@lzu.cn |
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