In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, so...Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.展开更多
A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some applica...A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.展开更多
In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscil...In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.展开更多
Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indica...Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indicated.展开更多
基金supported by the National Natural Science Foundation of China(No.60974025)
文摘In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
基金supported by the National Natural Science Foundation of China(No.60674020)
文摘In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
基金The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No.93-93-6)
文摘Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.
基金the Natural Science Foundation of Guangdong Pronvincial.
文摘A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.
文摘In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.
文摘Some new integral and discrete inequalities with power nonlinearity are established. Two recent results of B.G. Pachpatte are improved by some particularcorollaries of our results. Application examples are also indicated.
