Ground state solution on a non-autonomous Kirchhoff type equation

Existence of positive solutions for Kirchhoff-type problem in exterior domains

“…So a considerable effort has been devoted by many researcher in the whole space. We only focus on the type of Kirchhoff equations similar to Equation (1.1) now, namely, and its variants, where , , a > 0 and are constants, and is subcritical and superlinear near infinity (see, e.g., [11, 13, 17, 18, 20–22, 30, 31, 33, 34, 36]); one usually assumes that , or V ( x ) is periodic, or , or V ( x ) is coercive.…”

“…Particularly, the existence of solutions to Equation (1.2) and its variants was usually obtained by looking for the so-called ground states (see [11, 13, 17, 18, 20–22, 30, 31], etc). As we know, minimizing technique and the Mountain Pass Lemma are typical ways to deal with this problem.…”

“…In [11], Guo generalized the results in [13] by a new Nehari-Pohozaev manifold, while f may not be 4-superlinear at infinity. Later, using an abstract critical point theorem established by Jeanjean, authors of [20,21] showed the existence of positive ground-state solutions with Berestycki-Lions conditions, which improved the 4-superlinear conditions. The aim of this paper is to study the existence of positive solutions for Equation (1.1) in exterior domain Ω, with superlinear nonlinearities.…”

Existence of infinitely many solutions for a p-Kirchhoff problem in RN

“…where M(t) = α +βt with parameters α, β > 0, a < N-p p , h(x) and H(x) are nonnegative functions in R N , and further assumptions will be listed later. It is well known that problem like (1.1) originally comes from Kirchhoff 's important work [1], and Kirchhoff-type equations received much attention only after the paper by Lions [2]; see [3][4][5][6][7][8] and the references therein. Zhang and Perera [6] considered the following problem:…”

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

“…Because the Kirchhoff-type equation has a wide range of applications in many fields, such as it models several physical and biological systems, it has been widely considered in the last two decades by using variational methods, see [1][2][3][4][5][6][7][8][9][10][11] and references therein. We just introduce several results closely related to Equation (1) here.…”