Special issue "Variational and topological analysis: methods and applications"

The special issue Variational and topological analysis: methods and applications provides new existence and non-existence results for mathematical models via different equations, inequalities and inclusions driven by suitable principal operators.The classical variational and non-variational methods, as well as several consolidated numerical techniques, are adopted and adapted to increase the knowledge of the behavior and intrinsic properties of such mathematical models and their corresponding physical systems.In general, the problems collected in the special issue are studied imposing specific boundary conditions, and mild assumptions on the data and setting.The arguments used in the proofs and experiments pay attention to the difficulties originated by the nonlocal nature and the lack of regularity for the main operator and solution space, this makes the approach very specialized but effective.The fifteen contributions collected in the special issue reach results concerning existence, multiplicity and asymptotic behavior of solutions, as well as convergence statements, relevant in the context of optimization and control.We like to emphasize the investigations concerning the Schrödinger equation (Ziqing Yuan and Jing Zhao: Trudinger-Moser inequality, variational methods and Morse theory are used in obtaining the existence and multiplicity of solutions, Yong-Chao Zhang: variational methods are used in proving the existence of least energy solutions), hence different Kirchhoff-type equations (Wei Ma and Qiongfen Zhang: variational methods and critical point theory are used in establishing the existence of nontrivial solutions, Zhenluo Lou and Jian Zhang: variational methods, truncation techniques and steep potential well are used in proving the existence and concentration behavior of solutions), the cable equation (Mohamed Jleli and Bessem Samet: nonlinear capacity estimates are used in establishing sufficient conditions for the