Existence ground state solutions for a quasilinear Schrödinger equation with Hardy potential and Berestycki–Lions type conditions

2022 ◽  
Vol 123 ◽  
pp. 107615
Author(s):  
Die Hu ◽  
Qi Zhang
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Hardy Potential ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions

AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES

2018 ◽  
Vol 99 (2) ◽  
pp. 231-241
Author(s):  
SITONG CHEN ◽  
ZU GAO
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions

By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.

scholarly journals Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 779 ◽  
Author(s):  
Jianqing Chen ◽  
Qian Zhang
Keyword(s):  
Schrödinger Equation ◽  
Critical Exponent ◽  
Orlicz Space ◽  
Ground State ◽  
Schrodinger Equation ◽  
Nonlinear Term ◽  
Ground State Solution ◽  
Existence Results ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions

We study the following quasilinear Schrödinger equation involving critical exponent - Δ u + V ( x ) u - Δ ( u 2 ) u = A ( x ) | u | p - 1 u + λ B ( x ) u 3 N + 2 N - 2 , u ( x ) > 0 for x ∈ R N and u ( x ) → 0 as | x | → ∞ . By using a monotonicity trick and global compactness lemma, we prove the existence of positive ground state solutions of Pohožaev type. The nonlinear term | u | p - 1 u for the well-studied case p ∈ [ 3 , 3 N + 2 N - 2 ) , and the less-studied case p ∈ [ 2 , 3 ) , and for the latter case few existence results are available in the literature. Our results generalize partial previous works.

scholarly journals New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

2021 ◽  
pp. 1-17
Author(s):  
Yingying Xiao ◽  
Chuanxi Zhu
Keyword(s):  
Gauge Theory ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions ◽  
Chern Simons ◽  
Constraint Minimization

In this paper, we study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − κ u Δ ( u 2 ) + μ h 2 ( | x | ) | x | 2 ( 1 + κ u 2 ) u + μ ( ∫ | x | + ∞ h ( s ) s ( 2 + κ u 2 ( s ) ) u 2 ( s ) d s ) u = f ( u ) in   R 2 , κ > 0 V ∈ C 1 ( R 2 , R ) and f ∈ C ( R , R ) By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

Ground state solution for the Schrödinger equation with Hardy potential and critical Sobolev exponent

2021 ◽  
pp. 1-19
Author(s):  
Jing Zhang ◽  
Lin Li
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Critical Sobolev Exponent ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
State Solution ◽  
Hardy Potential ◽  
Asymptotically Periodic ◽  
Sobolev Exponent

In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

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