Critical Fujita Exponents for Nonlocal Reaction Diffusion Systems

In this paper, we prove the existence of critical Fujita exponents for a class of nonlocal reaction diffusion systems. And it is proved that the critical Fujita exponents belong to the blow up case.     

全空间上带Hardy-Sobolev项的拟线性椭圆方程解的存在性

讨论了全空间上一类带Hardy-Sobolev项的拟线性椭圆问题,利用集中紧原理和适当的实验函数,得到并验证了(PS)_c条件,从而证明了该问题非平凡解的存在性.     

Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball.We are interested in the critical global exponent q_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.     

Critical Quenching Exponents for Heat Equations Coupled with Nonlinear Boundary Flux

We discuss the quenching phenomena for a system of heat equations coupled with nonlinear boundary flux. We determine a critical value for the exponents in the boundary flux, such that only in the super critical case the simultaneous quenching can happen for any solution.     

一个具有非局部效应的非线性周期反应扩散方程的渐近形态

研究一个具有非线性-非局部反应的周期反应扩散系统.利用周期半流的渐近理论来讨论渐近波速c~*和周期行波解的存在性,证明参数c~*也是周期行波解的最小波速,并清晰描述解传播的阈值性质.最后给出渐近波速和最小波速c~*的估计.     

非线性发展方程非局部初值问题解的存在性

本文讨论非线性方程的非局部初值问题，利用半群理论、单调算子理论以及Banach不动点定理，分别得到两个问题的温和解和弱解的存在唯一性定理．     

Critical Nonlinear Nonlocal Equations on a Half-Line

We study nonlinear nonlocal equations on a half-line in the critical case

具临界Sobolev指数的半线性椭圆方程的多重正解

本文讨论了零边值半线性椭圆方程的多重正解，其中使用没有（ＰＳ）条件的山路引理及对最佳Ｓｏｂｏｌｅｖ嵌入常数的分析，证明了至少两个解的存在性．     

Propagation of Perturbations of Solutions for a Doubly Degenerate Nonlinear Parabolic Equation

ＰｒｏｐａｇａｔｉｏｎｏｆＰｅｒｔｕｒｂａｔｉｏｎｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＤｏｕｂｌｙＤｅｇｅｎｅｒａｔｅＮｏｎｌｉｎｅａｒＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＷａｎｇＹｉｆｕ（王一夫）；ＹｉｎＪｉｎｇｘｕｅ（尹景学）（Ｄｅｐａｒｔｍｅｎｔｏｆ...     

Solvability of a Mixed Nonlocal Problem for a Nonlinear Singular Viscoelastic Equation

The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems.     

The Darmon-Granville Equation with Algebraic Exponents

We will investigate solutions to the Darmon-Granville equation with Gaussian integer exponents.     

Morse Index and Critical Groups for p-Laplace Equations with Critical Exponents

In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index. Dedicated to the memory of Professor Aldo Cossu The research of the authors was supported by the MIUR project “Variational and topological methods in the study of nonlinear phenomena” (PRIN 2005).     

On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents

In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p < n, q ≥ [n(p - 1) + p]/(n - p), σ > 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.     

一类具非局部边界条件的四阶非线性微分方程的对称正解

本文考虑形如的非线性四阶微分方程非局部边值问题,这里a,b∈L~1[0,1],g:(0,1)→[0,∞)在(0,1)上连续、对称,且可能在t=0和t=1处奇异．f:[0,1]×[0,∞)→[0,∞)连续且对所有x∈[0,∞],f(·,x)在[0,1]上对称．在某些适当的增长性条件下,应用Krasnoselskii不动点定理证明了对称正解的存在性和多重性．