Positive stationary solutions and threshold results for the non-homogeneous semilinear parabolic equation with Robin boundary conditions

DOI10.1016/j.na.2013.02.028zbMath1280.35068arXiv1001.5221OpenAlexW2000017123MaRDI QIDQ387149

Huaxiang Hu, Jun-Hui Xie, Qiu-Yi Dai

Publication date: 19 December 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.5221

zbMATH Keywords

global solutionthreshold resultminimal stationary solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Initial-boundary value problems for second-order parabolic equations (35K20) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

Cites Work

• Unnamed Item
• Positive solutions of the Robin problem for semilinear elliptic equations on annuli
• Asymptotic behavior of some nonlinear heat equations
• A bound for global solutions of semilinear heat equations
• Existence and non-existence of global solutions for a semilinear heat equation
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
• A prior estimate and existence of positive solutions of semilinear elliptic equation with the third boundary value problem
• Elliptic partial differential equations of second order
• Existence of many positive solutions of semilinear equations on annulus
• Positive solutions of inhomogeneous elliptic equations with indefinite data
• Dual variational methods in critical point theory and applications
• Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications
• On potential wells and applications to semilinear hyperbolic equations and parabolic equations
• On the positive of boundary-value problems for a class of nonlinear differential equations
• Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
• A priori bounds for positive solutions of nonlinear elliptic equations
• On the stability and instability of positive steady states of a semilinear heat equation in ℝn
• On the Cauchy Problem for Reaction-Diffusion Equations
• Existence of multiple positive solutions for $$ - \Delta u = \lambda u + u^{\frac{{N + 2}}{{N - 2}}} + \mu f\left( x \right)*$$
• Positive solutions for non-homogeneous semilinear elliptic equations with data that changes sign
• Further study on a nonlinear heat equation

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