Nodal bound state of nonlinear problems involving the fractional Laplacian |
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| Authors: | Wei Long Longbo Lv |
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| Affiliation: | College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, P. R. China |
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| Abstract: | This paper is concerned with the following nonlinear fractional Schrödinger equation ![]() where ε>0 is a small parameter, V(x) is a positive function, 0<s<1, and  . Under some suitable conditions, we prove that for any positive integer k, one can construct a nonradial sign‐changing (nodal) solutions with exactly k maximum points and k minimum points near the local minimum point of V(x). |
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| Keywords: | fractional Laplacian nonlinear Schrö dinger equation reduction method |
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. Under some suitable conditions, we prove that for any positive integer k, one can construct a nonradial sign‐changing (nodal) solutions with exactly k maximum points and k minimum points near the local minimum point of V(x).