Ground state sign-changing solutions for fractional Kirchhoff equations in bounded domains

Abstract

We study the existence of ground state sign-changing solutions for the fractional Kirchhoff problem. Under mild assumptions on the nonlinearity, by using some new analytical skills and the non-Nehari manifold method, we prove that the fractional Kirchhoff problem possesses a ground state sign-changing solution ub. Moreover, we show that the energy of ub is strictly larger than twice that of the ground state solutions of Nehari-type. Finally, we establish the convergence property of ub as the parameter b ↘ 0. Our results generalize some results obtained by Shuai [J. Differ. Equations 259, 1256 (2015)] and Tang and Cheng [J. Differ. Equations 261, 2384 (2016)].

Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity

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Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity

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“…This fact makes the study of fractional Schrödinger-Maxwell-Kirchhoff systems and similar problems particularly interesting. A lot of interesting results on the existence of nonlocal problems were obtained recently in, for examples, [1,5,7,9,10,11,12,13,14,17,18,19,24,27,29] and the cited references.…”

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