Results 41 to 50 of about 447 (79)
Increasing powers in a degenerate parabolic logistic equation [PDF]
, 2012 The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \partial_t u-\Delta u=a u-b(x) u^p \text{in} \Omega\times \R^+, u(0)=u_0, u(t)|_{\partial \Omega}=0 $$ as $p\to +\infty$, where $\Omega$ is a ...
Hugo Tavares, Jose Francisco, Rodrigues
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Multiple positive solutions to a p-Kirchhoff equation with logarithmic terms and concave terms
Open MathematicsIn this article, we focus on a class of pp-Kirchhoff-type equations that include logarithmic and concave terms. By applying the variational method, we establish the existence and multiplicity of positive solutions.
Liang Jin-Ping, Wang Ran-Ran, Wang Yue
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Ground State for a Coupled Elliptic System with Critical Growth
Advanced Nonlinear Studies, 2018 We study the following coupled elliptic system with critical nonlinearities:
Wu Huiling, Li Yongqing
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Ground states of Schrödinger systems with the Chern-Simons gauge fields
Advanced Nonlinear Studies, 2023 We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui +4 more
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Transactions of the London Mathematical Society, 2021 In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
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Supercritical Hénon-type equation with a forcing term
Advances in Nonlinear AnalysisThis 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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, 2010 We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative ...
G. R. Grimmett +7 more
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Advanced Nonlinear StudiesThe 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 Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
, 2019 We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term.
Birindelli, Isabeau, Galise, Giulio
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Demonstratio MathematicaThis article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em ...
Huang Lanxin, Su Jiabao
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