Infinitely many solutions for indefinite quasilinear Schrödinger equations under broken symmetry situations |
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| Authors: | Liang Zhang Xianhua Tang Yi Chen |
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| Institution: | 1. School of Mathematical Sciences, University of Jinan, Jinan, Shangdong, China;2. School of Mathematics and Statistics, Central South University, Changsha, Hunan, China;3. Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China |
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| Abstract: | In this paper, we study the existence of infinitely many solutions for the indefinite quasilinear Schrödinger equations ![]() where α≥2,  . When g(x,u) is only of locally superlinear growth at infinity in u and h(x,u) is not odd in u, the existence of infinitely many solutions is proved in spite of the lack of the symmetry of this problem by using dual approach and Bolle's perturbation method. Our results generalize some known results and are new even in the symmetric situation. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | Bolle's perturbation method broken symmetry dual approach indefinite quasilinear Schrö dinger equation |
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. When g(x,u) is only of locally superlinear growth at infinity in u and h(x,u) is not odd in u, the existence of infinitely many solutions is proved in spite of the lack of the symmetry of this problem by using dual approach and Bolle's perturbation method. Our results generalize some known results and are new even in the symmetric situation. Copyright © 2016 John Wiley & Sons, Ltd.