Results 81 to 90 of about 160 (129)

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
openaire   +2 more sources

Pohozaev identity for the anisotropic $p$-Laplacian and estimates of torsion function

, 2018
In this paper we prove the Pohozaev identity for the weighted anisotropic $p$-Laplace operator. As an application of our identity, we deduce the nonexistence of nontrivial solutions of the Dirichlet problem for the weighted anisotropic $p$-Laplacian in star-shaped domains of $\mathbb{R}^n$. We also provide an upper bound estimate for the first Dirichet
Xia, Changyu, Wang, Qiaoling
openaire   +2 more sources

Existence of solution for asymptotically linear systems in R^N

Electronic Journal of Differential Equations, 2013
We show the existence of solution for a strongly coupled elliptic system under three different conditions, namely: the autonomous case, the radial case, and a general case. For the autonomous case, we present a characterization of the solution.
Raquel Lehrer
doaj  

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
doaj   +1 more source

Nonexistence and existence of solutions for a supercritical p-Laplacian elliptic problem

Advanced Nonlinear Studies
In this paper, we obtain a general supercritical Sobolev inequality in W0,rad1,p(B) ${W}_{0,rad}^{1, p}\left(B\right)$ , where B is the unit ball in RN ${\mathbb{R}}^{N}$ .
Liu Yanjun, Li Yu, Chen Yuan
doaj   +1 more source

Infinitely many solutions for nonlinear elliptic equations with degenerate coercivity

Electronic Journal of Qualitative Theory of Differential Equations
In this article, we consider the following quasilinear elliptic equation $$\begin{cases} -\operatorname{div}\dfrac{\nabla u}{(1+u)^{2\theta}} - \dfrac{\gamma\theta|\nabla u|^2}{(1+u)^{1+2\theta}} = u^p,\ x \in \mathbb{R}^N,\\[8pt] u > 0, \ \lim ...
Yongkuan Cheng, Yinchen Fan
doaj   +1 more source

Positive ground state solution for Kirchhoff equations with subcritical growth and zero mass

Electronic Journal of Differential Equations, 2015
In this article, we study the Kirchhoff equation $$\displaylines{ -\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^{2}dx\Big)\Delta u=K(x)f(u), \quad x\in \mathbb{R}^N,\cr u\in D^{1,2}(\mathbb{R}^N), }$$ where a>0, b>0 and $N\geq3$.
Yu Duan, Jiu Liu, Chun-Lei Tang
doaj  

The qualitative behavior at the free boundary for approximate harmonic maps from surfaces. [PDF]

Math Ann, 2019
Jost J, Liu L, Zhu M.
europepmc   +1 more source

On the energy partition in oscillations and waves. [PDF]

Proc Math Phys Eng Sci, 2015
Slepyan LI.
europepmc   +1 more source

Pohozaev identities and Kelvin transformation of semilinear Grushin equation

In this paper, we study Pohozaev identities, Kelvin transformation and their applications of semilinear Grushin equation. First, we establish two Pohozaev identities generated from translations and determine the location of the concentration point for solution of a kind of Grushin equation by such identities.
Wei, Yawei, Zhou, Xiaodong
openaire   +2 more sources