Results 21 to 30 of about 1,711 (146)
Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 In the current work, the modified (2 + 1)‐dimensional Hietarinta model is considered by employing Hirota’s bilinear scheme. Likewise, the bilinear formalism is obtained for the considered model. In addition, the periodic‐solitary, periodic wave, cross‐kink wave, and interaction between stripe and periodic wave solutions of the mentioned equation by ...
Guangping Li +5 more
wiley +1 more source
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
Unique continuation for the magnetic Schrödinger equation [PDF]
, 2020 The unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is ...
Benedicks, M., Laestadius, A., Penz, M.
core +2 more sources
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 +3 more
wiley +1 more source
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 +2 more
wiley +1 more source
Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects [PDF]
, 2015 This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained.
Liu, Wenbin, Shen, Tengfei
core +5 more sources
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
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
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
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