Results 71 to 80 of about 160 (129)

On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets

Advances in Nonlinear Analysis, 2019
We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, 0 < α < β < 1, of the involved nonlinearites ...
Díaz J.I., Hernández J., Ilyasov Y.Sh.
doaj   +1 more source

Pohozaev identities for a pseudo-relativistic Schrödinger operator and applications

, 2018
In this paper we prove a Pohozaev-type identity for both the problem $(-Δ+m^2)^su=f(u)$ in $\mathbb{R}^N$ and its harmonic extension to $\mathbb{R}^{N+1}_+$ when ...
Bueno, H., Pereira, G. A, Medeiros, A. H. Souza   +2 more
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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 Alexander   +1 more
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Integro-differential equations : regularity theory and Pohozaev identities

, 2023
The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and Sobolev inequalities. Integro-differential equations arise naturally in the study of stochastic processes with jumps, and are used in ...
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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
doaj  

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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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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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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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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