We consider two classes of nonlinear eigenvalue problems with double-phase energy and lack of compactness. We establish existence and non-existence results and related properties of solutions. Our analysis combines variational methods with the generalized Pucci-Serrin maximum principle. Remark: Nonlinear Analysis, Theory, Methods and Applications (published by Elsevier) is considered one of the leading journals in our field and our project group often published in this journal. By the Slovenian Research Agency criteria, this paper is a very high quality achievement, with the maximum possible score (A'=1).

COBISS.SI-ID: 18661465

We study existence of weak solutions for certain classes of nonlinear Schrödinger equations on the Poincaré ball model \mathbb{B}^N, N\ge 3. By using the Palais principle of symmetric criticality and suitable group theoretical arguments, we establish the existence of a nontrivial (weak) solution. Remark: Journal of Mathematical Analysis and Applications (published by Elsevier) is considered one of the leading journals in our field and our project group often published in this journal. By the Slovenian Research Agency criteria, this paper is a very high quality achievement, with the maximum possible score (A'=1).

COBISS.SI-ID: 25766659

The monograph emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1), and it is the most cited book in Mathematical Reviews among all monographs published in the year 2019.

COBISS.SI-ID: 18583897

The monograph develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolves in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 18463065

The aim of this monograph is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 18413657