Guanggang Liu, Shaoyun Shi, Yucheng Wei
Abstract:
In this article we consider elliptic equations whose nonlinear term
depends on the gradient of the unknown. We assume that the nonlinearity
has a asymptotically linear growth at zero and at infinity
with respect to the second variable. By applying Morse theory and
an iterative method, we prove the existence of nontrivial solutions.
Submitted April 17, 2012. Published August 19, 2012.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Semilinear equation; Morse theory; critical group; iterative method.
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Guanggang Liu College of Mathematics, Jilin University Changchun 130012, China email: lgg112@163.com |
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Shaoyun Shi College of Mathematics, Jilin University Changchun 130012, China email: shisy@jlu.edu.cn |
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Yucheng Wei College of Mathematics, Jilin University Changchun 130012, China. Department of Mathematics, Hechi University Yizhou 546300, China email: ychengwei@126.com |
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