Results 81 to 90 of about 159 (128)

Structure Results for Semilinear Elliptic Equations with Hardy Potentials

Advanced Nonlinear Studies, 2018
We prove structure results for the radial solutions of the semilinear ...
Franca Matteo, Garrione Maurizio
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Exponential Decay of the Solutions of Quasilinear Second-Order Equations and Pohozaev Identities

Journal of Differential Equations, 2000
The paper is devoted to a rather detailed study of the pointwise exponential decay of the solutions of quasilinear second-order equations, \[ -\sum\limits _{\alpha ,\beta =1}^{N}a_{\alpha \beta }(x,u,\nabla u)\partial_{\alpha }\partial_{\beta }u+b(x,u,\nabla u)=f \] on \(\mathbb{R}^N\) under general assumptions about the coefficients \(a_{\alpha \beta }
Rabier, Patrick J., Stuart, Charles A.
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Positive solutions for asymptotically 3-linear quasilinear Schrodinger equations

Electronic Journal of Differential Equations, 2020
In this article, we study the quasilinear Schrodinger equation $$ -\Delta u+V(x)u-\frac{\kappa}{2}[\Delta(1+u^2)^{1/2}]\frac{u}{(1+u^2)^{1/2}} =h(u),\quad x\in\mathbb{R}^N, $$ where $N\geq3$, $\kappa>0$ is a parameter, $V: \mathbb{R}^N\to\mathbb{R}$
Guofa Li, Bitao Cheng, Yisheng Huang
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Ground states for Schrödinger-Poisson system with zero mass and the Coulomb critical exponent

Advances in Nonlinear Analysis
This article focuses on the study of the following Schrödinger-Poisson system with zero mass: −Δu+ϕu=∣u∣u+f(u),x∈R3,−Δϕ=u2,x∈R3,\left\{\begin{array}{ll}-\Delta u+\phi u=| u| u+f\left(u),& x\in {{\mathbb{R}}}^{3},\\ -\Delta \phi ={u}^{2},& x\in {{\mathbb ...
Zhang Jing, Qin Dongdong, Sahara Siti, Wu Qingfang   +3 more
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Uniqueness of Single Peak Solutions for a Kirchhoff Equation

Mathematics
We deal with the following singular perturbation Kirchhoff equation: −ϵ2a+ϵb∫R3|∇u|2dyΔu+Q(y)u=|u|p−1u,u∈H1(R3), where constants a,b,ϵ>0 and ...
Junhao Lv, Shichao Yi, Bo Sun
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Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
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A note on a Pohozaev identity for the fractional Green function

We get a Pohozaev-type identity for the fractional Green function, which extends to the fractional setting a classical result by Brezis and Peletier. Our result complements with some more recent ones obtained by Djitte and Sueur concerning a representation formula for the gradient of the fractional Robin function.
Dieb, Abdelrazek, Ianni, Isabella
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Pohozaev identity for the fractional $p-$Laplacian on $\mathbb{R}^N$

, 2016
By virtue of a suitable approximation argument, we prove a Pohozaev identity for nonlinear nonlocal problems on $\mathbb{R}^N$ involving the fractional $p-$Laplacian operator. Furthermore we provide an application of the identity to show that some relevant levels of the energy functional associated with the problem coincide.
Brasco, Lorenzo, Mosconi, Sunra, Squassina, Marco   +2 more
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Solutions for fractional operator problem via local Pohozaev identities

, 2019
We consider the following fractional Schrödinger equation involving critical exponent: \begin{equation*} \left\{\begin{array}{ll} (-Δ)^s u+V(|y'|,y'')u=u^{2^*_s-1} \ \hbox{ in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. \end{equation*} where $s\in(\frac{1}{2}, 1)$, $(y',y'')\in \mathbb{R}^2\times \mathbb{R}^{N-2}$, $V(|y'|,y'')
Guo, Yuxia, Liu, Ting, Nie, Jianjun
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Multiplicity of Solutions for a Fractional Kirchhoff–Schrödinger Problem with Logarithmic Nonlinearity

Fractal and Fractional
In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional Kirchhoff–Schrödinger problem with logarithmic nonlinearity.
Xin Jin, Qiongfen Zhang, Xingwen Chen
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