Preface

hence it focuses on new existence and non-existence results of several classes of differential problems with structure constraints.The studies collected in the special issue are posed and solved in the appropriate abstract spaces, using and combining a variety of techniques.The strategy and methods of proofs need to be adapted to specific features of the involved operators.Hence, the authors have to overcome any lack of regularity with suitable technical hypotheses.The twelve contributions collected here, in Part I, focus both on the existence of certain notions of solutions and on the blow-up of solutions, hence the non-existence results.The developed approaches are applied in the case of elliptic, hyperbolic, and parabolic equations, as well as systems of equations.It is also worth mentioning the results of the differential inclusions, differential inequalities, and ordinary differential equations.Special attention is also paid to bifurcation analysis, stability of solutions, and equilibrium points, as well as to equivalence conditions for the main operators.The mathematical models investigated herein, aim to describe and represent physical situations where dynamical and evolution systems play a crucial role.We would like to express our thanks to all the authors for accepting our invitations to contribute to this special issue and sharing their works with readers.We thank all the valuable reviewers for their detailed and constructive comments.