## Leading-edge Research on Evolution EquationsThis book presents high-quality research from around the world on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. The book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations. |

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### Contents

1 | |

11 | |

19 | |

Internal Pollution and Discriminating Sentinel in Population Dynamics Problem | 29 |

Center Manifold and Stability in Critical Cases for Some Partial Functional Differential Equations | 49 |

Stability Radii of Positive Linear Functional Differential Systems in Banach Spaces | 77 |

Effects of Nonlocality and Phase Shift Definitions in Generalizing Levinsons Theorem | 101 |

Asymptotic Behavior of the FitzHughNagumo System | 131 |

A Partial Differential Equation with Nonautonomous Past Delay in LąPhase Space | 167 |

Solving the Hyperbolic Problem Obtained by Transmutation Operator | 185 |

Elliptic Operators with Variable Coefficients Generating Fractional Resolvent Families | 197 |

Existence Results for Pseudo Almost Periodic Differential Functional and Neutral Integral Equations | 207 |

237 | |

### Common terms and phrases

absorbing set Anal analytic semigroup Assume assumptions asymptotic stability Banach space bounded linear operator bounded set center manifold Co-semigroup complex condition consider continuous function continuum bound contour definition denote derivation dtdadx dxdt elliptic operator equation 1.1 equation with nonautonomous evolution equations existence and uniqueness exponential attractor exponentially stable FitzHugh-Nagumo FitzHugh-Nagumo equations fixed-point Fredholm determinants functional differential equations given global attractors Hence imaginary axis implies inequality integral equations integral solution Jost function JR JR Lemma Levinson's theorem Math Mathematics multi-perturbations nonautonomous past delay nonlinear nonlocal potential norm Nova Science Publishers obtain PAP(X partial differential equations partial functional partial functional differential periodic solutions phase shift phase space Phys poles pseudo almost periodic radius real axis result right-hand side satisfies semigroup sequence solution of equation solutions to Eq spurious stability radii transmutation operator uniformly weakly zeros of D(k