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A nonstandard Volterra integral equation on time scales

Reinfelds Andrejs, Christian Shraddha

Demonstratio Mathematica

2019

Vol. 52, nr 1

503--510

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

On bounded solutions of second order systems

Herzog G.

Demonstratio Mathematica

2006

Vol. 39, nr 4

793-801

We prove existence and uniqueness of bounded solutions of u"+f(t, u) = 0, u(0) = x on [0,infinity) under quasimonotonicity and one-sided Lipschitz conditions on f.