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Oscillation Criteria for Second Order Mixed Nonlinear Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 1049-1060页

作者： zhi-ting xu School of Mathematical Sciences South China Normal University

By using the refinement of the standard integral averaging technique, we obtain some oscillation criteria for second order mixed nonlinear elliptic equations. The results established in this paper extend and improve s... 详细信息

关键词： oscillation elliptic equations mixed nonlinear integral averaging technique

Oscillation of Second Order Semilinear Elliptic Equations with Damping

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2165-2178页

作者： zhi ting xu School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China

We obtain some new Kamenev-type oscillation theorems for the second order semilinear elliptic differential equation with damping N ∑i,j=1Di[aij（x）Djy]＋N∑i=1bi（x）Diy＋c（x）f（y）=0 under quite general assumptions. These results are extensions of the recent results of Sun [Sun, Y. G.： New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping. J. Math. Anal. Appl., 291, 341-351 （2004）] in a natural way. In particular, we do not impose any additional conditions on the damped functions bi （x） except the continuity. Several examples are given to illustrate the main results.

关键词： Oscillation damped semilinear elliptic differential equations second order

Averaging Technique for the Oscillation of Second Order Damped Elliptic Equations

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Acta Mathematica Sinica,English Series 2008年第5期24卷 829-842页

作者： zhi ting xu School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China

By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation N↑∑↓i,j=1 Di[AIY（x）Djy]＋N↑∑↓i=1 bi（x）Diy＋c（x）f（y）=0 which extend and... 详细信息

关键词： oscillation averaging technique second order elliptic differential equation damped

Oscillation Theorems for Nonlinear Second Order Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 569-578页

作者： zhi-ting xu School of Mathematical Sciences South China Normal University Guangzhou 510631 China

Some oscillation theorems are given for the nonlinear second order elliptic equation N∑i,j=1 Di[aij（x）ψ（y）｜｜△↓y｜｜^p-2 Djy]＋c（x）f（y）=0The results are extensions of modified Riccati techniques and inclu... 详细信息

关键词： Oscillation, nonlinear second order elliptic equation, Riccati techniques

Philos-type Oscillation Theorems for Second Order Damped Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 291-304页

作者： zhi-ting xu School of Mathematical Sciences South China Normal University Guangzhou 510631 China

Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equationΣi,j=1 N Di[aij（x）Djy]＋Σi=1 N bi（x）Diy＋c（x）f（y）=0under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of xu, Jia and Ma.

关键词： Oscillation elliptic differential equations second order damped

Traveling Waves for Nonlocal and Non-monotone Delayed Reaction-difusion Equations

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Acta Mathematica Sinica,English Series 2013年第11期29卷 2159-2180页

作者： zhi ting xu Pei xuan WENG School of Mathematical Sciences South China Normal University

We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c 〉 c. is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reactiondiffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature.

关键词： Nonlocal non-monotone delayed reaction-diffusion equation traveling wave solutions auxiliary equation

Oscillation of Second-order Quasilinear Neutral Delay Difference Equations

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Acta Mathematicae Applicatae Sinica 2011年第1期27卷 93-104页

作者： Dong-mei Wang zhi-ting xu College of Information Science Hainan University Haikou 570228 China School of Mathematical Science South China Normal University Guangzhou 510631 China

By using the Riccati transformation and mathematical analytic methods, some sufficient conditions are obtained for oscillation of the second-order quasilineoa＂ neutral delay difference equations

关键词： Oscillation Riccati transformation Difference equations

New Kamenev-type Oscillation Criteria for Half-linear Partial Differential Equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 535-548页

作者： Ge-feng YANG zhi-ting xu Cisco School of Informatics Guangdong University of Foreign StudiesGuangzhou510006China School of Mathematical Sciences South China Normal UniversityGuangzhou510631China

We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div（A（x）｜｜ u｜｜^p-2 u）＋〈b（x）,｜｜ u｜｜^p-2 u〉＋c（x）｜u｜^p-2u=0（E）under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 （2004） 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.

关键词： oscillation half-linear partial differential equations Kamenev-type Damped equation

Boundedness of Solutions of Second Order Nonlinear Dynamic Equations

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 505-520页

作者： Ye-hui HUANG zhi-ting xu School of Mathematical Sciences South China Normal University

This paper deals with the boundedness of the solutions of the following dynamic equations andon a time scale T. By using the Bellman integral inequality, we establish some sufficient conditions for bound- edness of solutions of the above equations. Our results not only unify the boundedness results for differential and difference equations but are also new for the q-difference equations.

关键词： boundedness nonlinear dynamic equations time scale solution second order