• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1235-1246
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• 2009

In this paper, we prove existence results for first order impulsive evolution differential inclusions with nonlocal condition by using a fixed point theorem for condensing multi-valued maps. An example is also given to illustrate the obtained results.

• 대한수학회지
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• 제50권1호
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• pp.41-59
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• 2013

In this paper, we investigate the existence and controllability results for a class of abstract stochastic evolution differential inclusions with nonlocal conditions where the linear part is nondensely defined and satisfies the Hille-Yosida condition. The results are obtained by using integrated semigroup theory and a fixed point theorem for condensing map due to Martelli.

• 대한수학회보
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• 제52권2호
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• pp.421-438
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• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.