临界非线性分数阶 SchrO¨dinger 方程变号解的存在性
Existence of Sign-Changing Solutions for a Critical Nonlinear Fractional SchrO¨dinger Equation
摘要: 本文主要研究了一类临界增长的分数阶 Schrödinger 方程变号解的存在性,其中0 < s < 1,N ≥ 3,是分数阶临界指数,µ是一个正常数,,ε > 0是一个小参数, V ∈ C1(RN , R)满足a ≤ V (x) ≤ b, b > a > 0 , ∀x ∈ RN.通过临界理论和下降流不变集法,我们得到了该方程存在k对变号解.
Abstract: In this paper, we study the following critical nonlinear fractional Schrödinger equations where 0 < s < 1,N ≥ 3, is the fractional critical exponent, µ is a normal number, , ε > 0 is a small parameter, V ∈ C1(RN , R) satisfies a ≤ V (x) ≤ b, b > a > 0 , ∀x ∈ RN . We obtain the existence of k pairs of sign-changing solutions by combining critical point theory and invariant sets of descending flow.
文章引用：黄娅林. 临界非线性分数阶 SchrO¨dinger 方程变号解的存在性[J]. 应用数学进展, 2021, 10(5): 1559-1585. https://doi.org/10.12677/AAM.2021.105166

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