Infinitely many nodal solutions with a prescribed number of nodes for the Kirchhoff type equations |
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Authors: | Hui Guo Ronghua Tang Tao Wang |
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Institution: | College of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China |
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Abstract: | In this paper, we investigate the existence of multiple radial sign-changing solutions with the nodal characterization for a class of Kirchhoff type problems where , are radial and bounded away from below by positive numbers. Under some weak assumptions on , by taking advantage of the Gersgorin disc's theorem and Miranda theorem, we develop some new analytic techniques and prove that this problem admits infinitely many nodal solutions having a prescribed number of nodes k, whose energy is strictly increasing in k. Moreover, the asymptotic behaviors of as are established. These results improve and generalize the previous results in the literature. |
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Keywords: | Nodal solutions Kirchhoff-type equations Nehari method Miranda theorem Disc's theorem |
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