## Partial Difference EquationsPartial Difference Equations treats this major class of functional relations. Such equations have recursive structures so that the usual concepts of increments are important. This book describes mathematical methods that help in dealing with recurrence relations that govern the behavior of variables such as population size and stock price. It is helpful for anyone who has mastered undergraduate mathematical concepts. It offers a concise introduction to the tools and techniques that have proven successful in obtaining results in partial difference equations. |

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### Contents

Basic Tools | 17 |

Symbolic Calculus | 47 |

Monotonicity and Convexity | 93 |

Explicit Solutions | 113 |

Stability | 147 |

Existence | 201 |

Nonexistence | 223 |

255 | |

266 | |

### Common terms and phrases

Assume by induction boundary conditions boundary value problem characteristic equation Cheng coefficients complex number component consider convergent convolution product corresponding solution delta sequence denoted discrete heat equation equal eventually positive solution Example existence finite domain formula frequency measures frequently negative frequently oscillatory frequently positive functional inequality given Green's function heat equation holds initial conditions initial value problem integer lattice points limsup linear lNxN lower solution matrix maximum principle method neighbors nonnegative integer nontrivial notation Note obtain ordinary difference equations ordinary operator partial difference equations positive numbers positive root proof is complete real bivariate sequence real numbers real sequence recurrence relation remark satisfies scalar Similarly solution of 6.37 solution pair spectral radius subsets unique solution upper degree upper solution variables vector view of Theorem Wirtinger's inequalities zero