The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

Liu, Yanjun; Liu, Chungen

doi:10.1007/s11401-022-0345-2

Cited by 2 publications

(1 citation statement)

References 29 publications

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“…A lot of interesting results on the existence of nonlocal problems were obtained recently in, for example, [4, 5, 7-9, 11, 13-17, 21, 25, 27-29] and the cited references. We especially refer to the paper [10] for the existence of ground state positive solutions of Kirchhoff-Schrödinger-type equations with singular exponential nonlinearities in R N .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Liu

Zhang

2020

Bound Value Probl

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In this paper, we consider the existence of a least energy nodal solution and a ground state solution, energy doubling property and asymptotic behavior of solutions of the following critical problem: $$ \textstyle\begin{cases} -(a+ b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\lambda \phi u= \vert u \vert ^{4}u+ k f(u),&x\in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2},&x\in \mathbb{R}^{3}. \end{cases} $$ { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u + λ ϕ u = | u | 4 u + k f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 . By nodal Nehari manifold method, for each $b>0$ b > 0 , we obtain a least energy nodal solution $u_{b}$ u b and a ground-state solution $v_{b}$ v b to this problem when $k\gg1$ k ≫ 1 , where the nonlinear function $f\in C(\mathbb{R},\mathbb{R})$ f ∈ C ( R , R ) . We also give an analysis on the behavior of $u_{b}$ u b as the parameter $b\to 0$ b → 0 .

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Liu

Zhang

2020

Bound Value Probl

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Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ^N

Mahanta,

Mukherjee,

Sarkar

2024

Forum Mathematicum

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In this paper, we deal with the existence of nontrivial nonnegative solutions for a ( p , N ) {(p,N)} -Laplacian Schrödinger–Kirchhoff problem in ℝ N {\mathbb{R}^{N}} with singular exponential nonlinearity. The main features of the paper are the ( p , N ) {(p,N)} growth of the elliptic operators, the double lack of compactness, and the fact that the Kirchhoff function is of degenerate type. To establish the existence results, we use the mountain pass theorem, the Ekeland variational principle, the singular Trudinger–Moser inequality, and a completely new Brézis–Lieb-type lemma for singular exponential nonlinearity.

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The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

Cited by 2 publications

References 29 publications

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ^N

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The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

Cited by 2 publications

References 29 publications

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N

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Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ^N