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Vicenţiu D. Rădulescu

Bio: Vicenţiu D. Rădulescu is an academic researcher from AGH University of Science and Technology. The author has contributed to research in topics: Nonlinear system & Mathematics. The author has an hindex of 46, co-authored 360 publications receiving 7771 citations. Previous affiliations of Vicenţiu D. Rădulescu include Romanian Academy of Sciences & Politehnica University of Bucharest.


Papers
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Book
26 Feb 2019
TL;DR: In this paper, the authors provide a thorough introduction to abstract methods used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators, as well as their applications to various processes arising in the applied sciences.
Abstract: This is the first of two volumes (the second will deal with applications) and it is focused on the interplay between pure and applied nonlinear analysis. The interest for this field in the last few decades has been huge, mainly because nonlinear analysis is the outgrowth of the needs of concrete problems arising in the applied sciences. In this volume the emphasis is on those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The next volume 2 will be devoted to the study of such problems. The contents of the first volume are divided into six chapters, plus a comprehensive list of references and subject index. This work provides researchers and graduate students with a thorough introduction to abstract methods used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. We 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. We demonstrate how all of these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book we maintain a good balance between rigorous mathematics and physical applications. The main benefits of this book are: (i) it is a bridge among several fields of mathematics; (ii) it illustrates the power of Sobolev spaces in nonlinear analysis; (iii) the methods are developed in their generality and can be extended to other classes of nonlinear problems; and (iv) it uses a modern, unified approach to analyzing nonlinear boundary value problems. The primary audience for this book are researchers in pure and applied nonlinear analysis and graduate students.

325 citations

Book
01 Jan 2008
TL;DR: In this paper, the authors consider singular Gierer-meinhardt systems and singular singular elliptic problems with singular nonlinear nonlinear convection terms and show that the influence of a nonlinear term in singular elliptical problems can influence the stability of the solution of a singular problem.
Abstract: II BLOW-UP SOLUTIONS 2 Blow-up solutions for semilinear elliptic equations 3 Entire solutions blowing-up at infinity for elliptic systems III ELLIPTIC PROBLEMS WITH SINGULAR NONLINEARITIES 4 Sublinear perturbations of singular elliptic problems 5 Bifurcation and asymptotic analysis The monotone case 6 Bifurcation and asymptotic analysis The nonmonotone case 7 Superlinear perturbations of singular elliptic problems 8 Stability of the solution of a singular problem 9 The influence of a nonlinear convection term in singular elliptic problems 10 Singular Gierer-Meinhardt systems A Spectral theory for differential operators B Implicit function theorem C Ekeland's variational principle D Mountain pass theorem References Index

245 citations

Journal ArticleDOI
TL;DR: In this paper, the qualitative analysis of solutions to nonlinear elliptic problems of the type { − div A (x, ∇ u ) = λ | u | q (x ) − 2 u in Ω u = 0 on ∂ Ω, where Ω is a bounded or an exterior domain of R N and q is a continuous positive function.
Abstract: In this survey paper, by using variational methods, we are concerned with the qualitative analysis of solutions to nonlinear elliptic problems of the type { − div A ( x , ∇ u ) = λ | u | q ( x ) − 2 u in Ω u = 0 on ∂ Ω , where Ω is a bounded or an exterior domain of R N and q is a continuous positive function. The results presented in this paper extend several contributions concerning the Lane–Emden equation and we focus on new phenomena which are due to the presence of variable exponents.

218 citations

Journal ArticleDOI
TL;DR: In this article, the existence of multiple ground state solutions for a class of parametric fractional Schrodinger equations whose simplest prototype is (−�) s u + V (x)u = λ f (x, u) in R n, where n > 2, s stands for the fractional Laplace operator of order s ∈ (0, 1),a ndλ is a positive real parameter.
Abstract: In this paper, we study the existence of multiple ground state solutions for a class of parametric fractional Schrodinger equations whose simplest prototype is (−�) s u + V (x)u = λ f (x, u) in R n , where n > 2 ,( −�) s stands for the fractional Laplace operator of order s ∈ (0,1) ,a ndλ is a positive real parameter. The nonlinear term f is assumed to have a superlinear behaviour at the origin and a sublinear decay at infinity. By using variational methods, we establish the existence of a suitable range of positive eigenvalues for which the problem admits at least two nontrivial solutions in a suitable weighted fractional Sobolev space. Mathematics Subject Classification 35A15 · 35S15 · 49J35 · 45G05 · 47G20

207 citations


Cited by
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Book ChapterDOI
01 Jan 2015

3,828 citations

Journal ArticleDOI
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

01 Jan 2016
TL;DR: The methods of modern mathematical physics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.

1,536 citations

Book ChapterDOI
01 Jan 2003
TL;DR: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas and there is no doubt that a modern treatise on “Nonlinear functional analysis” can not afford the luxury of ignoring multivalued analysis.
Abstract: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

996 citations

Book ChapterDOI
01 Jan 1985
TL;DR: The first group of results in fixed point theory were derived from Banach's fixed point theorem as discussed by the authors, which is a nice result since it contains only one simple condition on the map F, since it is easy to prove and since it nevertheless allows a variety of applications.
Abstract: Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

994 citations