Preface |
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1 | (22) |
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1 | (1) |
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1 | (5) |
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6 | (3) |
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Fixed Point Theorems and Auxiliary Results |
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9 | (3) |
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Preliminaries in a Banach Space |
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12 | (3) |
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15 | (2) |
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Measure of Noncompactness |
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17 | (1) |
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The Measure of Nonconvexity |
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18 | (4) |
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22 | (1) |
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23 | (50) |
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23 | (1) |
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Causal Functional and Differential Inequalities |
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24 | (3) |
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Existence and Extremal Solutions |
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27 | (5) |
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32 | (3) |
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35 | (5) |
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40 | (3) |
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Continuous Dependence Relative to Initial Data |
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43 | (4) |
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Existence of Euler Solutions |
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47 | (4) |
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51 | (2) |
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Systems of Causal Differential Inequalities |
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53 | (2) |
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Nonlinear Variation of Parameters |
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55 | (4) |
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Integral Equations of Sobolev Type |
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59 | (6) |
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Differential Equations of Sobolev Types |
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65 | (5) |
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70 | (3) |
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Theoretical Approximation Methods |
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73 | (32) |
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73 | (1) |
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Method of Lower and Upper Solutions |
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74 | (1) |
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Monotone Iterative Technique |
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75 | (4) |
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Generalized Monotone Iterative Technique |
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79 | (8) |
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Monotone Technique for PBVPs |
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87 | (4) |
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The Method of Quasilinearization (MQL) |
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91 | (3) |
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Extension of Quasilinearization |
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94 | (5) |
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Newton's Method Versus Quasilinearization |
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99 | (3) |
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102 | (3) |
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105 | (32) |
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105 | (1) |
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Comparison Theorems via Lyapunov Functions |
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106 | (5) |
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Definitions of Stability and Boundedness |
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111 | (3) |
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Definitions Relative to Two Measures |
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114 | (2) |
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Stability Criteria-Lyapunov Functions |
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116 | (2) |
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Stability Criteria-Lyapunov Functionals |
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118 | (2) |
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Lyapunov Functions on Product Spaces |
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120 | (3) |
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Stability in Terms of two Measures |
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123 | (2) |
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Vector Lyapunov Functions |
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125 | (3) |
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Cone-valued Lyapunov Functions |
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128 | (8) |
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136 | (1) |
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Miscellaneous Topics in Causal Systems |
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137 | (66) |
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137 | (1) |
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Causal Set Differential Equations |
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138 | (8) |
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Comparison Results and Stability Theory |
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146 | (11) |
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Causal Differential Equations in a Banach Space |
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157 | (6) |
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Global Existence and Inequalities in Cones |
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163 | (6) |
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Fractional Causal Differential Equations |
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169 | (6) |
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Causal Differential Equations with Memory |
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175 | (6) |
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Causal Differential Systems with Retardation and Anticipation |
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181 | (7) |
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Monotone Iterative Technique |
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188 | (5) |
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Neutral Differential Equations with Causal Operators on a Semi-Axis |
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193 | (8) |
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201 | (2) |
Bibliography |
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203 | (4) |
Subject Index |
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207 | |