Explanipedia

Nonexistence of solutions for tempered fractional parabolic equations Open

Honghong Huang, Yansheng Zhong · 2024

In this paper, we consider the following parabolic equations involving tempered fractional operators. Assume that the function $ h \in C(\mathbb{R}) $ to equation (1.1) is strictly increasing with respect to $ x_1 $ and satisfying $ h(0) =…

The long-time behavior of solitary waves for the weakly damped KdV equation Open

Yansheng Zhong, Riguang Wu · 2023

In this paper, we first introduce the long-time behavior stability of solitary waves for the weakly damped Korteweg–de Vries equation. More concretely, solutions of the dissipative system with the initial values near a $c_{0}$ -speed s…

On a p-Laplacian eigenvalue problem with supercritical exponent Open

Yansheng Zhong, Yongqing Li · 2018

In this paper, we prove the existence of the positive and negative solutions to p-Laplacian eigenvalue problems with supercritical exponent. This extends previous results on the problems with subcritical and critical exponents.

Exponential attractors for the strongly damped wave equations with critical exponent Open

Yansheng Zhong · 2016

In this paper, we prove the existence of global attractor and exponential attractor in some stronger spaces for the strongly damped nonlinear wave equation when the nonlinear term $f(u,u_{t})$ depends on $u_{t}$ and contains a critical exp…

Multiple solutions for the p-Laplacian problem with supercritical exponent Open

Yansheng Zhong · 2015

In this paper, we explore the existence of multiple solutions to the following p-Laplacian type of equation with supercritical Sobolev-exponent: $$ \begin{cases} -\Delta_{p} u+|u|^{r-2}u=\gamma|u|^{s-2}u &\mbox{in }\Omega,\\ u =0 &\mbox{on…

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