Results 61 to 70 of about 1,711 (146)
Nonexistence of stable solutions for quasilinear Schrödinger equation
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 +3 more
doaj +1 more source
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we study the existence of positive solutions for the following generalized quasilinear Schrödinger equation \begin{equation*} -\operatorname{div}(g^p(u)|\nabla u|^{p-2}\nabla u)+g^{p-1}(u)g'(u)|\nabla u|^p+V(x)|u|^{p-2}u =K(x)f(u)+Q(x)g(u)|
Zhen Li
doaj +1 more source
On the logarithmic Schrodinger equation
, 2013 In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic equations with ...
d'Avenia, Pietro +2 more
core +1 more source
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, we consider the following quasilinear p⟶⋅‐elliptic problems with flux boundary conditions of the type −∑i=1N∂/∂xiaix,∂u/∂xi+bxupMx−2u=f1x,u−sgnug1x in Ω,∑i=1Naix,∂u/∂xiνi=cxuqx−2u+f2x,u−sgnug2x on ∂Ω.. Using the Fountain theorem and dual Fountain theorem, we prove the existence and multiplicity of solutions for a given problem, subject ...
Ahmed Ahmed +2 more
wiley +1 more source
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
doaj +1 more source
Concentrating solutions for a fractional Kirchhoff equation with critical growth
, 2019 In this paper we consider the following class of fractional Kirchhoff equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll} \left(\varepsilon^{2s}a+\varepsilon^{4s-3}b\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right ...
Ambrosio, Vincenzo
core +1 more source
Asymptotically linear fractional Schrodinger equations
, 2014 By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically linear ...
Lehrer, Raquel +2 more
core +1 more source
Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this paper we construct an $O(2)$-equivarint Hopf bifurcation normal form for a model of a nonlinear optical system with delay and diffraction in the feedback loop whose dynamics is governed by a system of coupled quasilinear diffusion equation and ...
Stanislav Budzinskiy, Alexander Razgulin
doaj +1 more source
Controllability of the 1D Schrodinger equation by the flatness approach
, 2014 We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "
Martin, Philippe +2 more
core +3 more sources
Critical quasilinear Schrodinger equation with sign-changing potential
Electronic Journal of Differential Equations, 2016 We study the existence of nontrivial solutions for a class of quasilinear Schrodinger equations in R^N with critical nonlinearity, where the potential is allowed to change signs.
Li-Li Wang, Zhi-Qing Han
doaj