Results 71 to 80 of about 1,711 (146)

Multiplicity and concentration results for some nonlinear Schr\"odinger equations with the fractional $p$-Laplacian

, 2018
We consider a class of parametric Schr\"odinger equations driven by the fractional $p$-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth.
Ambrosio, Vincenzo, Isernia, Teresa
core   +1 more source

Existence of nontrivial solutions for a quasilinear Schrodinger equations with sign-changing potential

Electronic Journal of Differential Equations, 2014
In this article we consider the quasilinear Schrodinger equation where the potential is sign-changing. We employ a mountain pass argument without compactness conditions to obtain the existence of a nontrivial solution.
Xiang-Dong Fang, Zhi-Qing Han
doaj  

Concentration phenomena for critical fractional Schr\"odinger systems

, 2018
In this paper we study the existence, multiplicity and concentration behavior of solutions for the following critical fractional Schr\"odinger system \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s} (-\Delta)^{s}u+V(x) u=Q_{u}(u, v)+\frac{1 ...
Ambrosio, Vincenzo
core   +1 more source

Blow-up phenomena and asymptotic profiles passing from $H^1$-critical to super-critical quasilinear Schrödinger equations [PDF]

, 2021
Daniele Cassani, Youjun Wang
openalex   +1 more source

Local well-posedness for a quasilinear Schrödinger equation with degenerate dispersion [PDF]

, 2020
Benjamin Harrop‐Griffiths, Jeremy L. Marzuola   +1 more
openalex   +1 more source

Infinitely many solutions for a quasilinear Schrödinger equation with Hardy potentials

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this article, we study the following quasilinear Schr\"odinger equation \begin{equation*} -\Delta u-\mu\frac{u}{|x|^{2}}+V(x)u-(\Delta(u^{2}))u=f(x,u),\qquad x\in \mathbb{R}^{N}, \end{equation*} where $ V(x) $ is a given positive potential and the ...
Tingting Shang, Ruixi Liang
doaj   +1 more source

Stability of the determination of a time-dependent coefficient in parabolic equations

, 2012
We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x u+\sigma(t)f(x)u ...
Choulli, Mourad, Kian, Yavar
core   +3 more sources

Existence of solutions to quasilinear Schrodinger equations with indefinite potential

Electronic Journal of Differential Equations, 2015
In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(x)u-(|u| ^2)''u=f(u) $$ on $\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions
Zupei Shen, Zhiqing Han
doaj  

Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback [PDF]

, 2019
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system
Zhang, Christophe
core   +2 more sources

Soliton solutions for a quasilinear Schrodinger equation

Electronic Journal of Differential Equations, 2013
In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\Delta_p u-\frac{p}{2^{p-1}}u\Delta_p(u^2)=f(x,u) $$ in a bounded smooth domain $\Omega\subset\mathbb{R}^{N}
Duchao Liu
doaj