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Balachandran K.,Byszewski L.,Kim J. K. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
The aim of this paper is to prove the existence and uniqueness of mild and classical solutions of a second order evolution equation with functional dependence on the solutions and on derivatives of the solutions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied. Further we discuss the existence of solutions of nonlinear fractional differential equations in abstract spaces.