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Monotone Iterative Technique for a Class of Semilinear Evolution Equations with Nonlocal Conditions

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Abstract

This paper discusses the existence and uniqueness of mild solutions for a class of semilinear evolution equations with nonlocal conditions in an ordered Banach space E. Under some monotonicity conditions and noncompactness measure conditions of the nonlinearity, a new monotone iterative method on the evolution equations with nonlocal conditions has been established. Particularly, an existence result without using noncompactness measure condition is obtained in ordered and weakly sequentially complete Banach spaces, which is very convenient for application. An example to illustrate our main results is also given.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Pengyu Chen & Yongxiang Li

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  1. Pengyu Chen
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  2. Yongxiang Li
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Correspondence to Pengyu Chen.

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Research supported by NNSFs of China (10871160, 11061031) and Project of NWNU-KJCXGC-3-47.

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Chen, P., Li, Y. Monotone Iterative Technique for a Class of Semilinear Evolution Equations with Nonlocal Conditions. Results. Math. 63, 731–744 (2013). https://doi.org/10.1007/s00025-012-0230-5

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