Impulsive differential equations and inclusions

By Mouffak Benchohra, J. Henderson, Sotiris K. Ntouyas. 2006

1,054 citations recorded by the source corpus.

Dedication We dedicate this book to our family members who complete us. In particular, M. Ben-chohra's dedication is to his wife, Kheira, and his children, Mohamed, Maroua, and Abdelillah; J. Henderson dedicates to his wife, Darlene, and his descendants, Kathy, Contents Preface xi 1. Preliminaries 1 1.1. Definitions and results for multivalued analysis 1 1.2. Fixed point theorems 4 1.3. Semigroups 7 1.4. Some additional lemmas and notions 9 2. Impulsive ordinary differential equations & inclusions 11 2.1. Introduction 11 2.2. Impulsive ordinary differential equations 12 2.3. Impulsive ordinary differential inclusions 24 2.4. Ordinary damped differential inclusions 49 2.5. Notes and remarks 62 3. Impulsive functional differential equations & inclusions 63 3.1. Introduction 63 3.2. Impulsive functional differential equations 63 3.3. Impulsive neutral differential equations 74 3.4. Impulsive functional differential inclusions 80 3.5. Impulsive neutral functional DIs 95 3.6. Impulsive semilinear functional DIs 107 3.7. Notes and remarks 118 4. Impulsive differential inclusions with nonlocal conditions 119 4.1. Introduction 119 4.2. Nonlocal impulsive semilinear differential inclusions 119 4.3. Existence results for impulsive functional semilinear differential inclusions with nonlocal conditions 136 4.4. Notes and remarks 145 5. Positive solutions for impulsive differential equations 147 5.1. Introduction 147 5.2. Positive solutions for impulsive functional differential equations 147 5.3. Positive solutions for impulsive boundary value problems 154 5.4. Double positive solutions for impulsive boundary value problems 159 5.5. Notes and remarks 165 viii Contents 6. Boundary value problems for impulsive differential inclusions 167 6.1. Introduction 167 6.2. First-order impulsive differential inclusions with periodic boundary conditions 167 6.3. Upper-and lower-solutions method for impulsive differential inclusions with nonlinear boundary conditions 184 6.4. Second-order boundary value problems 191 6.5. Notes and remarks 198 7. Nonresonance impulsive differential inclusions 199 7.1. Introduction 199 7.2. Nonresonance first-order impulsive functional differential inclusions with periodic boundary conditions 199 7.3. Nonresonance second-order impulsive functional differential inclusions with periodic boundary conditions 209 7.4. Nonresonance higher-order boundary value problems for impulsive functional differential inclusions 217 7.5. Notes and remarks 227 8. Impulsive differential equations & inclusions with variable times 229 8.1. Introduction 229 8.2. First-order impulsive differential equations with variable times 229 8.3. Higher-order impulsive differential equations with variable times 235 8.4. Boundary value problems for differential inclusions with variable times 241 8.5. Notes and remarks 252 9. Nondensely defined impulsive differential equations & inclusions 253 9.1. Introduction 253 9.2. Nondensely defined impulsive semilinear differential equations with nonlocal conditions 253 9.3. Nondensely defined …

Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health

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Citations in the corpus

Stability and existence results for a class of nonlinear fractional differential equations with singularity (2018, neutral): “∫ 0 (s − θ)σ−1[ (θ)ψ1(θ,u(θ))]dθ ) ds (33)”
ASYMPTOTIC STABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY (2013, background): “Using fixed point approach, Luo [20] studied the asymptotic stability of mild solutions of stochastic partial differential equations with finite delays.”
Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, neutral): “(17) In the same fashion, one has ||G2(p, q)||PC ≤ (m + 1)α2 (MΨ + a2) r.”
Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions (2009, neutral): “[16], Lakshmikantham et al.”
Existence of solutions to boundary value problem for impulsive fractional differential equations (2014, background): “Such problems appear in mathematical models with suddenly changes of their states in population dynamics, pharmacology, optimal control, etc [19].”
On the new concept of solutions and existence results for impulsive fractional evolution equations (2011, background): “For a wide bibliography and exposition on this object see for instance the monographs of [1, 2, 3, 4] and the papers [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19].”