Results 1 to 10 of about 1,711 (146)

An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term [PDF]

Journal of Function Spaces, 2020
In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −divg2u∇u+gug′u∇u2+Vxu=λx−μ∗upup−2u,x∈ℝN, where N≥3, g:ℝ→ℝ+ is a C1 even function, g0=1, g′s≥0 is for all s≥0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α>1 ...
Quanqing Li, Kaimin Teng, Jian Zhang, Jianjun Nie   +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 global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions [PDF]

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
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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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Multiple small solutions for Schrödinger equations involving positive quasilinear term

Electronic Journal of Qualitative Theory of Differential Equations, 2020
We consider the multiplicity of solutions of a class of quasilinear Schrödinger equations involving the $p$-Laplacian: \begin{equation*} -\Delta_{p} u+V(x)|u|^{p-2}u+\Delta_{p}(u^{2})u=K(x)f(x,u),\qquad x\in \mathbb{R}^{N}, \end{equation*} where $\Delta_{
Dashuang Chong, Xian Zhang, Chen Huang
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Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity [PDF]

Boundary Value Problems, 2023
In this article, we study the quasilinear Schrödinger equation − △ ( u ) + V ( x ) u − △ ( u 2 ) u = g ( x , u ) , x ∈ R N , $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$ where the potential V ( x ) $V(x)$ and
Jiameng Li, Huiwen Chen, Zhimin He, Zigen Ouyang   +3 more
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Standing waves for quasilinear Schrödinger equations involving double exponential growth

AIMS Mathematics, 2023
We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation $ \begin{equation*} \left\lbrace\begin{array}{rcll} -{\rm div} \Big(\log \dfrac{e}{|x|}\nabla u\Big) -{\rm div} \Big(\log \dfrac{e}{
Yony Raúl Santaria Leuyacc
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Existence of weak solutions for quasilinear Schrödinger equations with a parameter

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper, we study the following quasilinear Schrödinger equation of the form \begin{equation*} -\Delta_{p}u+V(x)|u|^{p-2}u-\left[\Delta_{p}(1+u^{2})^{\alpha/2}\right]\frac{\alpha u}{2(1+u^{2})^{(2-\alpha)/2}}=k(u),\qquad x\in \mathbb{R}^{N}, \end ...
Yunfeng Wei, Caisheng Chen, Hongwei Yang, Hongwang Yu   +3 more
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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 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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