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
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 so...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.展开更多
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...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.展开更多
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...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 some existing oscillation criteria for half-linear PDE in the literature.展开更多
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 ...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.展开更多
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...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 include recent results of Usami.展开更多
基金Supported by the National Natural Science Foundation of Guangdong Province under Grant (No.8451063101000730)
文摘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
基金supported by the National Natural Science Foundation of China(11171120)the Natural Science Foundation of Guangdong Province(No:S2012010010034,S2013010013050)
文摘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.
基金Supported by the Natural Science Foundation of Guangdong Province(No.8451063101000730).
文摘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.
基金Supported by the Doctoral Program of Higher Education of China(20094407110001)
文摘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 some existing oscillation criteria for half-linear PDE in the literature.
基金Supported by the National Natural Science Foundation of Guangdong Province under Grant (No.8451063101000730)
文摘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.
文摘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 include recent results of Usami.
