Retarded Inequalities With Two Independent Variables For Retarded Partial Differential Equations
Keywords: Explicit bounds,retarded integral inequalities,two independent variables,global existence.
ABSTRACT: In this article some new two dimensional nonlinear integral inequalities are obtained. These inequalities can be used as ready and powerful tools in the analysis of various classes of partial differential, integral and integrodifferential equations. As an application of nonlinear integral inequalities with delay,global existence of nonlinear partial differential is presented.
L.OU-IANG, The boundedness of solution of linear differential equation y^''+A(t)y=0 . shuxue Jim zhan, Vol. 5, Part 3,1997, 409-415.
Y.H.Kim, On some new integral inequalities for functions one one and two variables. Acta Math. Sinica,21(2),( 2005),423-434.
B.G.Pachpatte, Inequalitios for Differential and Integral Equations. Acadamic press, New York,1998
B.G.Pachpatte, Explicit bounds on certain integral inequalities . J.Math.Anal.Appl,267,( 2002), 48-61.
M.C.Tan and E.H.Yang, Estimation of bounded solutions on integral inequalities involving infinite integration limits. J Inequal.pure and Appl. Math., 5(7), (2006),Art 189.
E.H.Yang M.C. Tan, A Generalization of Constantinís integral inequalities and its discrete analogue. Proc. Glasgow Mathematical Association, J Inequal.pure and Appl. Math., 8(2)(2007),Art 87.
Y.H.Kim, Gronwall, Bellman and Pachpatte type integral inequalities with applications. Nonlinear Analysis,71,(2009),e2641-e2656
W.N. Li, M.A.Han and F.W. Meng, Some new delay integral inequalities and their applications . J. comp.Appl.Math.,180,( 2005),191-200.
O. Lipovan,A retarded Gronwall-like inequality and applications. J.Math.Anal.Appl,252,(2000),389-401.
O. Lipovan,A retarded integral inequality and applications. J.Math.Anal.Appl,285,(2003),436-443.
O. Lipovan,Integral inequality for retarded Volterra equations. J.Math.Anal.Appl,322,(2006),349-358.
Q.H.Ma and E.H.Yang, On some new nonlinear delay integral inequalities . J.Math.Anal.Appl,252, (2000),864-878.
Q.H.Ma and J.Picaric,Some new nonlinear retarded integral inequalities and their applications . Math.Inequal and Applis,9(4) (2006),617-632.
Y.G.Sun, On retarded integral inequalities and their applications. J. Math. Anal. Appl, 301, (2005), 265-275.
Wu-Sheng Wang,Some retarded nonlinear integral inequalities and their applications in retarded differential equations.J.Inequal and Appl, 75, (2012), 1-8.