Existence and asymptotic behavior of positive ground state solutions for coupled nonlinear fractional Kirchhoff-type systems

Multiple positive solutions to the fractional Kirchhoff problem with critical indefinite nonlinearities

“…Xie-Chen [26] presented a multiplicity result on the Kirchhoff-type problems in the bounded domain by using a similar strategy. A number of works dealt with the fractional differential equations [3,6,7,11,21] and some recent results on problem (1.3) can be seen in [4,5,10,12,13,14,15,16,22,23,27] and the references therein.…”

Existence and multiplicity of positive solutions for fractional Laplacian systems with nonlinear coupling

“…Moreover, the asymptotic behavior of the solutions as β → 0 was also analyzed by them. For the other related results about the fractional Laplacian system, we refer the readers to [8,9,12] and the references therein. Motivated by [23,31,32,33,37], it is very natural for us to pose some questions, in particular, such as:…”

“…Moreover, the asymptotic behavior of the solutions as β → 0 was also analyzed by them. For the other related results about the fractional Laplacian system, we refer the readers to [8,9,12] and the references therein.…”

Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions

“…By using Pohozaev's identity, they obtained the existence, regularity, radial symmetry and decay property of a mountain pass solution to (1.2), depending on s and regularity of f when f satisfies Berestycki-Lions type condition. For the case that f (x, u) = K(x)|u| p−2 u + Q(x)|u| q−2 u with 2 < q < p < 2 * s , where 2 * s = 6 3−2s is the fractional critical Sobolev exponent, by using the Mountain pass theorem and Ljusternik-Schnirelmann theory, Shang and Zhang [25] showed the existence and multiplicity results to the fractional Schrödinger equation (1.2) with competing potential functions. After that, Zhang, Wang and Ji [35] generalized the result in [25] with f (x, u) = λh(x, u) + g(x)|u| 2 * s −2 u.…”

“…In the past few decades, many authors have conducted extensive research on problem (1.3), see, for example [6,15,16,17,18,31,32,36] and the references therein.…”