| On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian |
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| 作者姓名： | Zhi-hui Chen Yao-tian Shen |
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| 作者单位： | Zhi-hui Chen，Yao-tian ShenDepartment of Applied Mathematics，South China University of Technology，Guangzhou 510640，China |
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| 基金项目： | the National Natural Science Foundation of China (No.19871030)，the Guangdong Provincial Natural Science Foundation of China (No.980587). |
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| 摘 要： | In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.
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On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian |
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| Zhi-hui Chen,Yao-tian Shen.On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian[J].Acta Mathematicae Applicatae Sinica,2002(4). |
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| Authors: | Zhi-hui Chen Yao-tian Shen |
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| Institution: | Zhi-hui Chen,Yao-tian ShenDepartment of Applied Mathematics,South China University of Technology,Guangzhou 510640,China |
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| Abstract: | |
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| Keywords: | Quasi-asymptotically linear weak solution critical point Palais-Smale type condition |
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