On The Schrodinger Equation Involving A Critical Sobolev Exponent And Magnetic Field
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| Author | : Thierry Cazenave |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 516 |
| Release | : 2007-08-10 |
| Genre | : Mathematics |
| ISBN | : 3764374012 |
This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.
| Author | : Vincenzo Ambrosio |
| Publisher | : Springer Nature |
| Total Pages | : 669 |
| Release | : 2021-04-19 |
| Genre | : Mathematics |
| ISBN | : 3030602206 |
This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.
| Author | : Cyril Tintarev |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 230 |
| Release | : 2020-02-10 |
| Genre | : Mathematics |
| ISBN | : 3110532433 |
Concentration compactness methods are applied to PDE's that lack compactness properties, typically due to the scaling invariance of the underlying problem. This monograph presents a systematic functional-analytic presentation of concentration mechanisms and is by far the most extensive and systematic collection of mathematical tools for analyzing the convergence of functional sequences via the mechanism of concentration.
| Author | : Nikolaos S. Papageorgiou |
| Publisher | : Springer |
| Total Pages | : 586 |
| Release | : 2019-02-26 |
| Genre | : Mathematics |
| ISBN | : 3030034305 |
This book 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 nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
| Author | : Matthew J. Gursky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2009-06-26 |
| Genre | : Mathematics |
| ISBN | : 3642016731 |
This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
| Author | : Kyril Tintarev |
| Publisher | : World Scientific |
| Total Pages | : 279 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 1860946666 |
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces.Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
| Author | : |
| Publisher | : |
| Total Pages | : 380 |
| Release | : 2007 |
| Genre | : Differential equations |
| ISBN | : |
| Author | : Themistocles M. Rassias |
| Publisher | : Springer Nature |
| Total Pages | : 484 |
| Release | : 2021-02-26 |
| Genre | : Mathematics |
| ISBN | : 3030617327 |
This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.
| Author | : |
| Publisher | : |
| Total Pages | : 414 |
| Release | : 2005 |
| Genre | : Nonlinear functional analysis |
| ISBN | : |
| Author | : Pammy Manchanda |
| Publisher | : Springer Nature |
| Total Pages | : 431 |
| Release | : 2020-02-04 |
| Genre | : Mathematics |
| ISBN | : 981150928X |
This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.
