Results 1 to 10 of about 275,911 (150)

Existence of Nontrivial Solutions and High Energy Solutions for a Class of Quasilinear Schrödinger Equations via the Dual-Perturbation Method [PDF]

Abstract and Applied Analysis, 2013
We study the quasilinear Schrödinger equation of the form , . Under appropriate assumptions on and , existence results of nontrivial solutions and high energy solutions are obtained by the dual-perturbation method.
Yu Chen, Xian Wu
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Nonexistence of stable solutions for quasilinear Schrödinger equation [PDF]

Boundary Value Problems, 2018
In this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1 −Δu−[Δ(1+u2)1/2]u2(1+u2)1/2=h(x)|u|q−1u,x∈RN, $$ -\Delta u- \bigl[\Delta\bigl(1+u^{2}\bigr)^{1/2} \bigr]\frac{ u}{2(1+u^{2})^{1/2}}=h(x) \vert u ...
Lijuan Chen, Caisheng Chen, Hongwei Yang, Hongxue Song   +3 more
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Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space [PDF]

Mathematics, 2019
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
Jianqing Chen, Qian Zhang
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Existence and asymptotic properties of positive solutions for a general quasilinear Schrödinger equation [PDF]

Boundary Value Problems, 2019
By a change of variables with cut-off functions, we study the existence and the asymptotic behavior of positive solutions for a general quasilinear Schrödinger equation which arises from plasma physics. We extend the results of (Adv. Nonlinear Stud. 18(1)
Xiang Zhang, Yimin Zhang
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About existence and regularity of positive solutions for a quasilinear Schrödinger equation with singular nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2020
We establish the existence of positive solutions for the singular quasilinear Schrödinger equation \begin{equation*} \begin{cases} -\Delta u -\Delta (u^{2})u=h(x) u^{-\gamma} + f(x,u)& \mbox{in } \Omega,\\ u(x)=0&\mbox{on }\partial \Omega, \end{cases ...
Ricardo Alves, Mariana Reis
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Antisymmetric solutions for a class of quasilinear defocusing Schrödinger equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper we consider the existence of antisymmetric solutions for the quasilinear defocusing Schrödinger equation in $H^1(\mathbb{R}^N)$: $$ -\Delta u +\frac{k}{2}u \Delta u^2+V(x)u=g(u), $$ where $N\geq 3$, $V(x)$ is a positive continuous potential,
Janete Soares Gamboa, Jiazheng Zhou
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On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Frontiers in Physics, 2023
In this paper, we consider the non-existence and existence of solutions for a generalized quasilinear Schrödinger equation with a Kirchhoff-type perturbation.
Guofa Li, Chong Qiu, Bitao Cheng, Wenbo Wang   +3 more
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Existence of infinitely many normalized radial solutions for a class of quasilinear Schrödinger-Poisson equations in R³

AIMS Mathematics, 2022
In this paper, we study the existence of infinitely many normalized radial solutions for the following quasilinear Schrödinger-Poisson equations: $ \begin{equation*} -\Delta u-\lambda u+(|x|^{-1}*|u|^2)u-\Delta(u^2)u-|u|^{p-2}u = 0,\; x\in\mathbb{R}^
Jinfu Yang, Wenmin Li, Wei Guo, Jiafeng Zhang   +3 more
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Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity

AIMS Mathematics, 2023
In this paper, we investigate the existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity.
Xiaojie Guo, Zhiqing Han
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Soliton solutions for a class of generalized quasilinear Schrödinger equations

AIMS Mathematics, 2021
In this paper, critical point theory is used to show the existence of nontrivial solutions for a class of generalized quasilinear Schrödinger equations $ \begin{equation*} -\Delta_pu-{|u|}^{\sigma-2}uh'({|u|}^\sigma)\Delta_ph({|u|}^\sigma) = f(x,u ...
Rui Sun
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