Generalized retarded nonlinear integral inequalities involving iterated integrals and an application

In this work, some new generalized retarded nonlinear integral inequalities, which include nonlinear composite functions of unknown functions between iterated integrals, are discussed. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of differential-integral equations and some practical problems in engineering.MSC:26D15, 26D20, 34A12.

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

[2]  Yong Li,et al.  Nonlinear Retarded Integral Inequalities with Two Variables and Applications , 2010 .

[3]  Ravi P. Agarwal,et al.  Generalization of a retarded Gronwall-like inequality and its applications , 2005, Appl. Math. Comput..

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

[5]  Young-Ho Kim.  On Some New Integral Inequalities for Functions in One and Two Variables , 2005 .

[6]  B. G. Pachpatte,et al.  ON CERTAIN NONLINEAR INTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRALS , 2006 .

[7]  Side wall anodization of aluminum thin film on silicon substrate , 2005 .

[8]  Ravi P. Agarwal,et al.  New Integral Inequalities for Iterated Integrals with Applications , 2007 .

[9]  ON CERTAIN NEW INTEGRAL INEQUALITIES AND THEIR APPLICATIONS , 2002 .

[10]  Wu-Sheng Wang,et al.  A New Nonlinear Retarded Integral Inequality and Its Application , 2010 .

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

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

[13]  Yeol Je Cho,et al.  ON SOME INTEGRAL INEQUALITIES WITH ITERATED INTEGRALS , 2006 .

[14]  Byung-Il Kim.  ON SOME GRONWALL TYPE INEQUALITIES FOR A SYSTEM INTEGRAL EQUATION , 2005 .

[15]  ON SOME ADVANCED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS , 2005 .

[16]  J. Pečarić,et al.  ON CERTAIN NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES FOR FUNCTIONS IN TWO VARIABLES AND THEIR APPLICATIONS , 2008 .

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

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

[19]  W. Cheung,et al.  On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications , 2005 .

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

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

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

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

[24]  A. Abdeldaim,et al.  On some new integral inequalities of Gronwall-Bellman-Pachpatte type , 2011, Appl. Math. Comput..