Some generalized nonlinear retarded integral inequalities with applications

In this article we discuss some new generalized nonlinear Gronwall-Bellman-Type integral inequalities with two variables, which include a non-constant term outside the integrals. We use our result to deal with the estimate on the solutions of partial differential equations with the initial and boundary conditions.Mathematics Subject Classification 2000: 26D10; 26D15; 26D20; 34A40.

[1]  Hiroyuki Usami,et al.  Asymptotic behavior of solutions of a class of second order nonlinear differential equations , 1986 .

[2]  D. Bainov,et al.  Integral Inequalities and Applications , 1992 .

[3]  B. G. Pachpatte,et al.  Inequalities for differential and integral equations , 1998 .

[4]  E. V. Massalitina On the Perov Integro-Summable Inequality for Functions of Two Variables , 2004 .

[5]  I. Bihari A generalization of a lemma of bellman and its application to uniqueness problems of differential equations , 1956 .

[6]  Young Ho Kim,et al.  Some integral inequalities for functions of two variables , 2003 .

[7]  M. Pinto,et al.  On the asymptotic behavior of solutions of certain second order nonlinear differential equations , 1988 .

[8]  Sung Kyu Choi,et al.  NONLINEAR INTEGRAL INEQUALITIES OF BIHARI-TYPE WITHOUT CLASS H , 2005 .

[9]  R. Bellman The stability of solutions of linear differential equations , 1943 .

[10]  Qing-Hua Ma,et al.  Some new Gronwall-Bellman-Bihari type integral inequalities with delay , 2002, Period. Math. Hung..

[11]  B. G. Pachpatte ON SOME NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES , 2004 .

[12]  Wu-Sheng Wang Some new nonlinear Gronwall-Bellman-Type integral inequalities and applications to BVPs , 2011 .

[13]  Olivia Lipovan A Retarded Gronwall-Like Inequality and Its Applications , 2000 .

[14]  F. Dannan Integral Inequalities of Gronwall-Bellman-Bihari Type and Asymptotic Behavior of Certain Second Order Nonlinear Differential Equations , 1985 .

[15]  Josip Pečarić,et al.  Inequalities Involving Functions and Their Integrals and Derivatives , 1991 .

[16]  Wu-Sheng Wang,et al.  On a Generalized Retarded Integral Inequality with Two Variables , 2008 .

[17]  C. Dafermos The second law of thermodynamics and stability , 1979 .

[18]  Wing-Sum Cheung Some new nonlinear inequalities and applications to boundary value problems , 2006 .

[19]  Wing-Sum Cheung,et al.  Gronwall-Bellman-Type Integral Inequalities and Applications to BVPs , 2009 .

[20]  Wu-Sheng Wang A generalized retarded Gronwall-like inequality in two variables and applications to BVP , 2007, Appl. Math. Comput..

[21]  B. G. Pachpatte On Some New Inequalities Related to Certain Inequalities in the Theory of Differential Equations , 1995 .

[22]  T. H. Gronwall Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .

[23]  Ravi P. Agarwal,et al.  New Retarded Integral Inequalities with Applications , 2008 .