Multiplicity and asymptotic behavior of solutions for quasilinear elliptic equations with small perturbations |
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Authors: | Chen Huang |
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Institution: | College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou, 350117, PR China |
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Abstract: | This paper considers the following general form of quasilinear elliptic equation with a small perturbation: where is a bounded domain with smooth boundary and small enough. We assume the main term in the equation to have a mountain pass structure but do not suppose any conditions for the perturbation term . Then we prove the equation possesses a positive solution, a negative solution and a sign-changing solution. Moreover, we are able to obtain the asymptotic behavior of these solutions as . |
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Keywords: | Quasilinear elliptic equations Variational methods Asymptotic behavior |
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