Results 51 to 60 of about 95 (88)

Uniqueness for a semilinear elliptic equation in non-contractive domains under supercritical growth conditions

Electronic Journal of Differential Equations, 1999
We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in $Bbb R^n$ and establish uniqueness results for the smooth solutions of the Dirichlet problem for $-Delta u+|u|^{p-1}u=0$.
Kewei Zhang
doaj  

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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Classification of stable solutions for non-homogeneous higher-order elliptic PDEs

Journal of Inequalities and Applications, 2017
Under some assumptions on the nonlinearity f, we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of R n $\mathbb {R}^{n}$ for the following semilinear higher-order problem: ( − Δ ) k u = f ...
Abdellaziz Harrabi, Belgacem Rahal, Mohamed Karim Hamdani   +2 more
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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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Existence of solutions for a class of quasilinear Schrödinger equations with Choquard-type nonlinearity

Advances in Nonlinear Analysis
For the following quasilinear Choquard-type equation: −Δu−Δ(u2)u+V(x)u=(Iμ*∣u∣p)∣u∣p−2u,x∈RN,-\Delta u-\Delta \left({u}^{2})u+V\left(x)u=\left({I}_{\mu }* {| u| }^{p}){| u| }^{p-2}u,\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N≥3 ...
Shen Zifei, Yang Ning
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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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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
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Solutions to the Prescribed Positive Q-Curvature Equation with Power-Law Singular Terms in ${\mathbb{R}}^4$

Axioms
This paper investigates the solution theory of a class of prescribed positive Q-curvature equations with power-law singularity at the origin and polynomial growth at infinity in the four-dimensional Euclidean space. We focus on the equation involving the
Dejun Tai, Zixin Ren, Yumei Xing
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On the existence of a priori bounds for positive solutions of elliptic problems, I

Revista Integración, 2019
This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations (P)p     -\Delta_p u =f(u),  in  \Omega,    u = 0, on \partial\Omega widening the known ranges of subcritical ...
Rosa Pardo
doaj  

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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