TITLE:
A Least Energy Sign-Changing Solution for Nonlocal Schrödinger Equations with Asymptotically Linear Nonlinearities
AUTHORS:
Ni Li
KEYWORDS:
Nonlocal Schrödinger Equations, Least Energy Sign-Changing Solution, Integro-Differential Operator, Asymptotically Linear, Energy Doubling
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.6,
June
12,
2025
ABSTRACT: In this paper, we are concerned with the following nonlocal Schrödinger equations
−
ℒ
K
u+V(
x
)u=f(
x,u
), x∈
ℝ
N
,
where
−
ℒ
K
is an integro-differential operator of fractional Laplacian type and
V
is coercive at infinity. Combining the Nehari manifold and the quantitative deformation lemma, a least energy sign-changing solution was obtained, and the energy doubling phenomenon was also found.