Weak solutions for the dynamic Cauchy problem in Banach spaces

DOI10.1016/j.na.2009.01.175zbMath1198.34192OpenAlexW2094632719MaRDI QIDQ923954

Mieczysław Cichoń, Aneta Sikorska-Nowak, Ahmet Yantir, Ireneusz Kubiaczyk

Publication date: 24 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.01.175

zbMATH Keywords

weak solutionsmeasure of noncompactnessBanach spacetime scaleCauchy dynamic problem

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Applications of operator theory to differential and integral equations (47N20) Differential inequalities involving functions of a single real variable (34A40) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08) Dynamic equations on time scales or measure chains (34N05)

Related Items

Weak and pseudo-solutions of an arbitrary (fractional) orders differential equation in nonreflexive Banach space ⋮ A Cauchy Problem on Time Scales with Applications ⋮ General Cauchy–Lipschitz theory for Δ-Cauchy problems with Carathéodory dynamics on time scales ⋮ Weak solutions for fractional differential equations via Henstock-Kurzweil-Pettis integrals ⋮ Impulsive nonlocal differential equations through differential equations on time scales ⋮ Dynamic equations x(Δm)(t) = f(t, x(t)) on time scales ⋮ Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces ⋮ A note on Peano's theorem on time scales ⋮ Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals ⋮ Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

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