Recommended by Tomas Domínguez BenavidesBy constructing a structure operator quite different from that ofZhang and Baker 2000 and using the Schauder fixed point theory, the existence and uniqueness of the C 1 solutions of the series-like iterative equations with variable coefficients are discussed.
This paper investigates integral inequalities with delay for discontinuous functions involving two nonlinear terms. We do not require the classes ℘ and j in Gallo and Piccirillo's paper (Bound. Value Probl. 2009:808124, 2009). Our main results can be applied to generalize Gallo and Piccirillo's results and Iovane's results (Nonlinear Anal., Theory Methods Appl. 66:498-508, 2007). Examples to show the bounds of solutions of an impulsive differential equation are also given, which can not be estimated by Gallo and Piccirillo's results. MSC: 26D15; 26D20
This paper investigates integral inequalities for discontinuous functions with two independent variables involving two nonlinear terms. We do not require that ω(u) is in the class ℘ or the class j in Gallo and Piccirllo's paper (Nonlinear Stud. 19:115-126, 2012). My main results can be applied to generalize Borysenko and Iovane's results (Nonlinear Anal., Theory Methods Appl. 66:2190-2230 and to give results similar to Gallo-Piccirllo's. Examples to show the bounds of solutions of a partial differential equation with impulsive terms are also given, which cannot be estimated by Gallo and Piccirllo's results. MSC: 26D15; 26D20
This paper investigates some generalized Gronwall-Bellman type impulsive integral inequalities containing integration on infinite intervals. Some new results are obtained, which generalize some existing conclusions. Our result is also applied to study a boundary value problem of differential equations with impulsive terms.
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