High energy solutions of systems of Kirchhoff-type equations onRN

Existence and multiplicity of solutions for the Kirchhoff equations with asymptotically linear nonlinearities

“…Motivated by [9], we want to prove that the existence and multiplicity of solutions of problem (P) when nonlinear term f is an asymptotically linear nonlinearities. [10][11][12][13][14][15][16][17][18][19][20]12,21,22]. There still a large number of references to the Kirchhoff equations with non-constant potential V (x) which has a compactness property for the functional (1) corresponded to the problem (P).…”

Low energy small solutions of systems of Kirchhoff-type equations on RN

“…Recently, Wu 14 obtained a sequence of high energy solutions of system (1). After presenting a new proof technique, Zhou et al 16 improved the results obtained in Wu. 14 Motivated largely by the work of Zhou et al, 16 we are going to study the low energy solutions of system (1) by the variational approaches in this paper.…”

Existence and multiplicity of systems of Kirchhoff‐type equations with general potentials

“…Later, under the conditions ( V 0 ) and , Zhou, Wu, and Wu in presented a new proof technique to conclude the existence of high energy solutions for problem under some assumptions that are weaker than those in , which unify and sharply improve the Theorems 3.1–3.3 in as well as some results in other literature such as Theorems 1–4 in .…”

“…Equations like (1.1) in the whole space R N have also been studied extensively, for example, see [2,[9][10][11][12][13][14][15][16][17][18][19] and the references therein. In [9], Huang and Liu established the existence and nonexistence for Kirchhoff-type equations when f .x, u/ D juj p 2 u and p 2 .2, 6/ via variational methods.…”