Results 61 to 70 of about 160 (129)

Existence of regular and singular bound state solutions to a quasilinear equation

Boundary Value Problems
The existence of regular and singular bound state solutions to △ p u + f ( u ) = 0 , r ∈ R n ∖ { 0 } $$ \triangle _{p}u+f(u)=0,~~~r\in \mathbb{R}^{n}\backslash \{0\} $$ is considered. Our result concerns the solution according to its behavior as r → 0 $r\
Wei-Chuan Wang
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Existence of a ground-state solution for a quasilinear Schrödinger system

Frontiers in Physics
In this paper, we consider the following quasilinear Schrödinger system.−Δu+u+k2Δ|u|2u=2αα+β|u|α−2u|v|β,x∈RN,−Δv+v+k2Δ|v|2v=2βα+β|u|α|v|β−2v,x∈RN,where k < 0 is a real constant, α > 1, β > 1, and α + β < 2*.
Xue Zhang, Jing Zhang, Jing Zhang, Jing Zhang   +3 more
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The Pohozaev identity for mixed local-nonlocal operators

Journal of Mathematical Analysis and Applications
15 ...
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BEST CONSTANTS AND POHOZAEV IDENTITY FOR HARDY–SOBOLEV-TYPE OPERATORS

Communications in Contemporary Mathematics, 2013
This paper is threefold. Firstly, we reformulate the definition of the norm induced by the Hardy inequality (see [J. L. Vázquez and N. B. Zographopoulos, Functional aspects of the Hardy inequality. Appearance of a hidden energy, preprint (2011); http://arxiv.
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Nonlocal elliptic equations with mixed fractional Laplacians: stability and nonexistence results

Frontiers in Applied Mathematics and Statistics
In this study, we investigate the non-existence of solutions to the non-linear elliptic equation involving mixed fractional Laplacians: (-Δ)s1u+(-Δ)s2u=|u|p-1u in ℝn,where n ≥ 2s1, 0 < s2 < s1 < 1, and p > 1.
Akram Al-Muraqab, Cherif Zaidi, Imed Bouzida, Imed Bouzida, Imed Bouzida   +4 more
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Boundary charges and integral identities for solitons in (d+1)-dimensional field theories

Nuclear Physics B, 2017
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions.
Sven Bjarke Gudnason, Zhifeng Gao, Yisong Yang   +2 more
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Fractional Hadamard formulas, Pohozaev type identities and applications

, 2022
The thesis is composed of four Chapters. In the first Chapter, the boundary expression of the one-sided shape derivative of nonlocal Sobolev best constants is derived. As a simple consequence, we obtain the fractional version of the so-called Hadamard formula for the torsional rigidity and the first Dirichlet eigenvalue.
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Hardy inequality and Pohozaev identity for operators with boundary singularities: Some applications [PDF]

Comptes Rendus. Mathématique, 2011
We consider the Schrödinger operator A λ : = − Δ − λ /
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth

Advances in Nonlinear Analysis
We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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The Pohozaev identity for the Spectral Fractional Laplacian

15 ...
Barrios-Cubas, Itahisa, Bonforte, Matteo, González, María del Mar, Torres-Latorre, Clara   +3 more
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