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For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Multiple solutions for semilinear subelliptic Dirichlet problem。
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
In order to understand and identify key issues of food waste and find potential solutions for food waste minimization in food service business, both a questionnaire and a qualitative study were conduc...
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
In this talk, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation, the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation and the mKdV-...
In this talk, we investigate the fractalization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. The e...
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
In this talk, we consider nontrivial solutions of a quasilinear elliptic system with the weight functions h(x) and f_i (x) (i = 1, 2) by applying the Nehari manifold method along with the fibrering ma...
The theory of tetragonal curves is established and first applied to the study of algebro-geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature equation and the dis...
The talk is about applications of bilinear approaches to N-soliton solutions in (2+1)-dimensions. The Hirota N-soliton condition will be analyzed, together with novel examples of (2+1)-dimensional sol...
In this talk, we will focus on the classification of positive solutions to the critical p-Laplace equation. It is well known that such issue is crucial in many applications such as a priori estimates,...
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0inds of blowup solutions in this equation. I...

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