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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.

Second order evolution equations with nonlocal conditions

Benchohra M., Nieto J. J., Rezoug N.

Demonstratio Mathematica

2017

Vol. 50, nr 1

309--319

In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.