Results 21 to 30 of about 275,930 (166)

Ground state sign-changing solutions for a class of quasilinear Schrödinger equations

Open Mathematics, 2021
In this paper, we consider the following quasilinear Schrödinger equation: −Δu+V(x)u+κ2Δ(u2)u=K(x)f(u),x∈RN,-\Delta u+V\left(x)u+\frac{\kappa }{2}\Delta \left({u}^{2})u=K\left(x)f\left(u),\hspace{1.0em}x\in {{\mathbb{R}}}^{N}, where N≥3N\ge 3, κ>0\kappa \
Zhu Wenjie, Chen Chunfang
doaj   +1 more source

Dispersive Riemann problems for the Benjamin–Bona–Mahony equation

Studies in Applied Mathematics, Volume 147, Issue 3, Page 1089-1145, October 2021., 2021
Abstract Long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin‐Bona‐Mahony (BBM) equation are studied using asymptotic methods and numerical simulations. The catalog of solutions of the dispersive Riemann problem for the BBM equation is much richer than for the related, integrable, Korteweg‐de ...
T. Congy, G. A. El, M. A. Hoefer, M. Shearer   +3 more
wiley   +1 more source

Positive radial solutions for a class of quasilinear Schrödinger equations in $\mathbb{R}^3$

Electronic Journal of Qualitative Theory of Differential Equations, 2022
This paper is concerned with the following quasilinear Schrödinger equations of the form: \begin{equation*} -\Delta u-u\Delta (u^2)+u=|u|^{p-2}u, \qquad x\in \mathbb{R}^3, \end{equation*} where $p\in\left(2,12\right)$.
Zhongxiang Wang, Gao Jia, Weifeng Hu
doaj   +1 more source

Global Existence and Blow‐Up for the Classical Solutions of the Long‐Short Wave Equations with Viscosity

Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021
We are concerned with the global existence of classical solutions for a general model of viscosity long‐short wave equations. Under suitable initial conditions, the existence of the global classical solutions for the viscosity long‐short wave equations is proved. If it does not exist globally, the life span which is the largest time where the solutions
Jincheng Shi, Shengzhong Xiao, Nikos I. Karachalios   +2 more
wiley   +1 more source

Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions

Boundary Value Problems, 2020
In this article, we study a modified maximum principle approach under condition on the weight of the delay term in the feedback and the weight of the term without delay.
Yisheng Hu, Songhai Qin, Zhibin Liu, Yi Wang   +3 more
doaj   +1 more source

Positive solutions for a class of generalized quasilinear Schrödinger equation involving concave and convex nonlinearities in Orilicz space

Electronic Journal of Qualitative Theory of Differential Equations, 2021
In this paper, we study the following generalized quasilinear Schrödinger equation \begin{equation*} -\text{div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=\lambda f(x,u)+h(x,u),\qquad x\in\mathbb{R}^N, \end{equation*} where $\lambda>0$, $N\geq3$, $g\in\
Yan Meng, Xianjiu Huang, Jianhua Chen
doaj   +1 more source

Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials

Boundary Value Problems, 2021
In this paper, we study the following quasilinear Schrödinger equation: − div ( a ( x , ∇ u ) ) + V ( x ) | x | − α p ∗ | u | p − 2 u = K ( x ) | x | − α p ∗ f ( x , u ) in  R N , $$ -\operatorname{div}\bigl(a(x,\nabla u)\bigr)+V(x) \vert x \vert ...
Yan Meng, Xianjiu Huang, Jianhua Chen
doaj   +1 more source

Asymptotic behavior of multiple solutions for quasilinear Schrödinger equations

Electronic Journal of Qualitative Theory of Differential Equations, 2022
This paper establishes the multiplicity of solutions for a class of quasilinear Schrödinger elliptic equations: \begin{equation*} -\Delta u+V(x)u-\frac{\gamma}{2}\Delta(u^{2})u=f(x,u),\qquad x\in \mathbb{R}^{3}, \end{equation*} where $V(x):\mathbb{R}^3 ...
Xian Zhang, Chen Huang
doaj   +1 more source

Positive solutions for a critical quasilinear Schrödinger equation

AIMS Mathematics, 2023
In our current work we investigate the following critical quasilinear Schrödinger equation $ -\Delta \Theta+\mathcal V(x)\Theta-\Delta (\Theta^2)\Theta = |\Theta|^{22^*-2}\Theta+\lambda \mathcal K(x)g(\Theta), \ x \ \in \mathbb R^N, $ where $ N ...
Liang Xue , Jiafa Xu, Donal O'Regan
doaj   +1 more source

Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition

AIMS Mathematics, 2020
We study a quasilinear Schrödinger equation with Robin boundary condition. Using the variational methods and the truncation techniques, we prove the existence of two positive solutions when the parameter λ is large enough. We also establish the existence
Yin Deng, Gao Jia, Fanglan Li
doaj   +1 more source