Extremal solutions and comparison principle for nonlinear integro-differential equations in a Banach space

DOI10.1007/BF02560045zbMath0790.45013OpenAlexW1997399143MaRDI QIDQ5288871

Wan Zhuang, Yubo Chen

Publication date: 20 June 1994

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02560045

zbMATH Keywords

comparison principlenormal conemeasure of noncompactnessextremal solutionsnonlinear integro-differential equationordered Banach spacemaximal and minimal solutions

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Other nonlinear integral equations (45G10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Abstract integral equations, integral equations in abstract spaces (45N05)

Cites Work

• On the Cauchy problem for ordinary differential equations in Banach spaces
• On the method of upper and lower solutions in abstract cones
• Existence and uniqueness of solutions of nonlinear integro-differential equations of volterra type in a banach space
• The existence of maximal and minimal solution of the nonlinear integrodifferential equation in banach space
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