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We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero. [ABSTRACT FROM AUTHOR]

We consider a Schrödinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter. [ABSTRACT FROM AUTHOR]

We provide a new characterization of the logarithmic Sobolev inequality. [ABSTRACT FROM AUTHOR]

We investigate a class of nonlinear nonautonomous scalar field equations with fractional diffusion, critical power nonlinearity and a subcritical term. The involved potentials are allowed for vanishing behavior at infinity. The problem is set on the whole space and compactness issues have to be tackled. [ABSTRACT FROM AUTHOR]

We prove a Bourgain–Brézis–Mironescu-type formula for a class of nonlocal magnetic spaces, which builds a bridge between a fractional magnetic operator recently introduced and the classical theory. [ABSTRACT FROM AUTHOR]

We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding. [ABSTRACT FROM AUTHOR]

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric. The semi-linear problems are studied in a framework where the associated functional is of class C¹ but not of class C². [ABSTRACT FROM AUTHOR]

Abstract: We obtain the existence and uniqueness, regularity and boundary behavior for a class of singular quasi-linear elliptic equations in a smooth bounded domain. [Copyright &y& Elsevier]

For a class of minimization problems, where the functionals are weakly lower semicontinuous, we present, through the treatment of some semi-linear or quasi-linear type problems, techniques to show the existence of a minimizer. [ABSTRACT FROM AUTHOR]

Guest Editors: Vieri Benci Dipartimento di Matematica, Universit a di Pisa Via Filippo Buonarroti 1/C, 56127 Pisa, Italy vieri.benci@unipi.it Sunra Mosconi Dipartimento di Matematica e Informatica, Universit a di Catania Viale A. Doria 6, 95125 Catania, Italy sunra.mosconi@unict.it Marco Squassina Dipartimento di Matematica e Fisica, Universit a Cattolica del Sacro Cuore Via dei Musei 41, I-25121 Brescia, Italy marco.squassina@unicatt.it i Copyright of Discrete & Continuous Dynamical Systems- Series S is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. DISCRETE AND CONTINUOUS doi:10.3934/dcdss.2020446 DYNAMICAL SYSTEMS SERIES S Volume 14, Number 5, May 2021 pp. i{i PREFACE: APPLICATIONS OF MATHEMATICAL ANALYSIS TO PROBLEMS IN THEORETICAL PHYSICS This issue of DCDS-S contains selected contributions on the applications of mathematical analysis to various problems of theoretical physics, by leading experts in the eld. [Extracted from the article]