Abstract:We study the existence of mild solutions to differential inclusions with nonlocal conditions. The first result is established when evolution system is equicontinuous and multifunction is upper semi-continuous. Then another result is obtained when evolution system is not equicontinuous and not compact. The measure of noncompactness and the fixed point theorem for multivalued mappings play key roles in the proof. An example is provided to illustrate our results.
The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition η(0)∈∫0σΔs,η(s)ds, where Δ is a multi-valued map. Relative compactness of the set ∫0σΔs,η(s)ds in L2(0,ε),R is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.
The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition η(0)∈∫0σΔs,η(s)ds, where Δ is a multi-valued map. Relative compactness of the set ∫0σΔs,η(s)ds in L2(0,ε),R is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.
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