This paper is concerned with the existence and uniqueness of global strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. We assume that the linear part is a positive definite selfadjoint operator, and the nonlinear part satisfies some essential growth conditions. The discussions are based on analytic semigroups theory, the piecewise regular method and relevant fixed point theorem. The results obtained in this paper improve and extend some related conclusions on this topic. An example to illustrate the feasibility of our abstract results is also given.
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The authors would like to thank the anonymous referees for their carefully reading the manuscript and very important comments and suggestions that improved the results and quality of this paper. P. Chen acknowledge support from NNSF of China (No. 11501455) and Key Project of Gansu Provincial National Science Foundation (No. 1606RJZA015). Y. Li acknowledge support from NNSF of China (No. 11661071).
Byszewski, L.: Application of preperties of the right hand sides of evolution equations to an investigation of nonlocal evolution problems. Nonlinear Anal. 33(5), 413–426 (1998)MathSciNetCrossRefMATHGoogle Scholar
Byszewski, L.: Existence and uniqueness of a classical solutions to a functional-differential abstract nonlocal Cauchy problem. J. Math. Appl. Stoch. Anal. 12(1), 91–97 (1999)MathSciNetCrossRefMATHGoogle Scholar
Chen, P., Li, Y.: Monotone iterative technique for a class of semilinear evolution equations with nonlocal conditions. Results Math. 63(3), 731–744 (2013)MathSciNetCrossRefMATHGoogle Scholar
Corduneanu, C.: Principles of Differential and Integral Equations. Allyn and Bacon, Boston (1971)MATHGoogle Scholar