Existence of extremal mild solutions for the initial value problem of evolution equations with non-instantaneous impulses

DOI10.1007/s11784-017-0467-4zbMath1386.34112OpenAlexW2744382370MaRDI QIDQ1684907

Xuping Zhang, Pengyu Chen, Yongxiang Li

Publication date: 12 December 2017

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-017-0467-4

zbMATH Keywords

evolution equationmild solutionmonotone iterative techniquenon-instantaneous impulseslower and upper mild solutions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Nonlinear differential equations in abstract spaces (34G20) Functional-differential equations in abstract spaces (34K30) Impulsive partial differential equations (35R12)

Related Items (8)

Existence of solutions of non-autonomous fractional differential equations with integral impulse condition ⋮ Semilinear fractional differential equations with infinite delay and non-instantaneous impulses ⋮ Lipschitz stability of nonlinear ordinary differential equations with non-instantaneous impulses in ordered Banach spaces ⋮ Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions ⋮ Implicit Caputo fractional q-difference equations with non instantaneous impulses ⋮ 𝒮‐asymptotically 𝓌‐periodic mild solutions for noninstantaneous impulsive integro‐differential equations with state‐dependent delay ⋮ Non-autonomous evolution equations of parabolic type with non-instantaneous impulses ⋮ Non-autonomous parabolic evolution equations with non-instantaneous impulses governed by noncompact evolution families

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