Results 41 to 50 of about 526 (85)

Weak and stationary solutions to a Cahn–Hilliard–Brinkman model with singular potentials and source terms

Advances in Nonlinear Analysis, 2020
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn–Hilliard–Brinkman (CHB) system with an elliptic reaction-diffusion equation for a nutrient.
Ebenbeck Matthias, Lam Kei Fong
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Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

Advances in Nonlinear Analysis, 2021
Our purpose of this paper is to study positive solutions of Lane-Emden ...
Ma Yong, Wang Ying, Ledesma César T.
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Conformally covariant parameterizations for relativistic initial data

, 2016
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems.
Delay, Erwann
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Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential

Advanced Nonlinear Studies, 2020
Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
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A concentration phenomenon for semilinear elliptic equations

, 2012
For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$.
A.V. Buryak, Andrzej Szulkin, C.A. Stuart, C.A. Stuart, C.A. Stuart, C.A. Stuart, D. Bonheure, D.G. Costa, D.R. Smith, H. Berestycki, H. Brézis, J. López-Gómez, J.B. Pendry, Nils Ackermann, P.M. Girão, V.M. Shalaev, Y.V. Kartashov   +16 more
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Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

Advanced Nonlinear Studies, 2020
We consider periodic solutions of the following problem associated with the fractional Laplacian: (-∂x⁢x)s⁢u⁢(x)+∂u⁡F⁢(x,u⁢(x))=0{(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in ℝ{\mathbb{R}}.
Feng Zhenping, Du Zhuoran
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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
core  

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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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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