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Monotone iterative technique for non-autonomous semilinear differentia equations with nonlocal condition

Meraj Arshi, Pandey Dwijendra Narain

Demonstratio Mathematica

2019

Vol. 52, nr 1

29--39

The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.

Semicontinuous solutions of systems of functional equations

Herzog G.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(2)

207-219

We use the method of upper and lower solutions to prove the existence of upper and lower semicontinuous solutions of functional equations of the form F(w,u(w),u(g_1(w)),...,u(g_m(w)) = ) in R^n under monotonicity and quasimonotonicity assumptions on F, and for w from a metrizable topological spaces.