Differential And Difference Equations With Applications

The aim of this reprint is to highlight the significance of difference equations and their applications in applied mathematics. Difference equations provide a robust and widely recognized framework for modeling complex dynamical systems. In recent years, non-integer order derivative operators have gained attention, particularly for understanding anomalous behaviors in social and physical sciences. The following Special Issue introduces several important developments, including new partial fractional derivatives, a novel nonlinear delayed integral inequality for studying integro-differential equations, and a neural network approach for solving nonlinear partial differential equations. The existence and uniqueness of solutions for nonlinear differential equations with impulses at variable times are discussed, as well as the oscillatory behavior of nonlinear second-order differential equations. Ultimately, this reprint bridges theory and application, offering novel insights with a focus on differential and difference equations.

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook.