Results 41 to 50 of about 516 (74)

Supercritical Hénon-type equation with a forcing term

Advances in Nonlinear Analysis
This article is concerned with the structure of solutions to the elliptic problem for a Hénon-type equation with a forcing term: −Δu=α(x)up+κμ,inRN,u>0,inRN,(Pκ)\hspace{11.3em}-\Delta u=\alpha \left(x){u}^{p}+\kappa \mu ,\hspace{1.0em}\hspace{0.1em}\text{
Ishige Kazuhiro, Katayama Sho
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A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart

, 2020
We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
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The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
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Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Advances in Nonlinear Analysis
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
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The existence and boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms

Advances in Nonlinear Analysis, 2014
In this paper, for more general f, g and a, b, we obtain conditions about the existence and boundary behavior of solutions to boundary blow-up elliptic problems ▵u=a(x)g(u)+b(x)f(u)|∇u|q,x∈Ω,u|∂Ω=+∞$ \triangle u=a(x)g(u)+ b(x) f(u)|\nabla u|^q,\quad x\in
Zhang Zhijun
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Elliptic equations involving general subcritical source nonlinearity and measures [PDF]

, 2014
In this article, we study the existence of positive solutions to elliptic equation (E1) $$(-\Delta)^\alpha u=g(u)+\sigma\nu \quad{\rm in}\quad \Omega,$$ subject to the condition (E2) $$u=\varrho\mu\quad {\rm on}\quad \partial\Omega\ \ {\rm if}\ \alpha=1 ...
Chen, Huyuan, Felmer, Patricio, Véron, Laurent   +2 more
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Extremal values of the (fractional) Weinstein functional on the hyperbolic space

, 2016
We study Weinstein functionals, first defined in [33], mainly on the hyperbolic space ℍ n
Mukherjee, M.
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Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity

Advances in Nonlinear Analysis, 2018
We study the semilinear elliptic ...
Ghergu Marius, Kim Sunghan, Shahgholian Henrik   +2 more
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Semilinear fractional elliptic equations with gradient nonlinearity involving measures [PDF]

, 2013
We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where $\epsilon=1$ or
Chen, Huyuan, Veron, Laurent
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Boundary regularity, Pohozaev identities, and nonexistence results

, 2017
In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $\Omega$, $u\equiv0$ in $\mathbb R^n\backslash\Omega$. We first discuss in detail the boundary regularity of solutions, stating the main known results
Ros-Oton, Xavier
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