Existence of mild solutions for abstract semilinear evolution equations in Banach spaces

DOI10.1016/J.NA.2011.08.019zbMath1235.34174OpenAlexW2089658065MaRDI QIDQ644189

Tao Zhu, Chao Song, Gang Li

Publication date: 3 November 2011

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.2011.08.019

zbMATH Keywords

semigroupmeasure of noncompactnessmild solutionnonlocal conditions

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Applications of operator theory to differential and integral equations (47N20)

Related Items (17)

Nonlocal integro-differential equations without the assumption of equicontinuity on the resolvent operator in Banach spaces ⋮ Existence of mild solutions and controllability of fractional impulsive integrodifferential systems with nonlocal conditions ⋮ Existence of solutions for nonlinear mixed type integro-differential functional evolution equations with nonlocal conditions ⋮ Existence of solutions for nonlinear mixed type integrodifferential functional evolution equations with nonlocal conditions ⋮ On impulsive delay integrodifferential equations with integral impulses ⋮ Existence of mild solutions for a semilinear integrodifferential equation with nonlocal initial conditions ⋮ Unnamed Item ⋮ Existence of mild solutions for the impulsive semilinear nonlocal problem with random effects ⋮ Existence of mild solutions for a class of non-autonomous evolution equations with nonlocal initial conditions ⋮ Nonlocal solutions of parabolic equations with strongly elliptic differential operators ⋮ A study of nonlocal problems of impulsive integrodifferential equations with measure of noncompactness ⋮ Existence of mild and classical solutions for nonlocal impulsive integrodifferential equations in Banach spaces with measure of noncompactness ⋮ Mild solutions of non-autonomous second order problems with nonlocal initial conditions ⋮ Fractional non-autonomous evolution equation with nonlocal conditions ⋮ Stability for a class of fractional partial integro-differential equations ⋮ Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness ⋮ Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
• Multivalued perturbations of \(m\)-accretive differential inclusions
• Global existence for semilinear evolution equations with nonlocal conditions
• Global solutions of nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces
• Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces
• Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space
• Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
• Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions
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