A note on the existence of time periodic solution of a superlinear heat equation

Abstract

In this paper, we consider the existence of positive periodic solutions for a superlinear heat equation $u_t-\mathrm{\Delta }u=a(t)u^p$ with $1<p<p_s-1$ and $p_s$ being the Sobolev critical exponent, subject to homogeneous Dirichlet boundary condition. We relax the technical assumption on a(t) and convex assumption on the domain $\mathrm{\Omega }$, which generalizes the previous results.

Keywords:

• Superlinear
• heat equation
• time periodic solution

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Haochuan Huang’s research is supported by the Innovation Project of Graduate School of South China Normal University [2017LKXM016]; SCNU [2016YN12]. Jingxue Yin’s research is supported by NSFC [11771156]. Chunhua Jin’s research is supported by NSFC [11471127], [11571380]; Guangdong Natural Science Funds for Distinguished Young Scholar [2015A030306029].