Abstract
In this paper, we consider a new kind of Kirchhoff-type equation which is stated in the introduction. Under certain assumptions on potentials, we prove by variational methods that the equation has at least a ground state solution and investigate the asymptotic behavior of solutions.
Highlights
We investigate the existence and asymptotic behavior of ground state solutions in the following Kirchhoff-type equation:
He proved the existence of a positive ground state solution to (5) without any (A − R)type conditions
In [14], the authors obtained the existence of a nontrivial solution for the following Kirchhoff-type equation:
Summary
We investigate the existence and asymptotic behavior of ground state solutions in the following Kirchhoff-type equation: We assume that the function g ∈ C(R, R) satisfies the following: (g1) there exist constants C0 > 0 and p ∈ (2, 2∗], such that |g(t)| ≤ C0(1 + |t|p−1), Many scholars have studied the existence of nontrivial solutions for the Kirchhoff-type problem: There are still few results on the existence of a ground state solution to (2) without an (A − R) condition (see [11–13]).
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