947 research outputs found
Semilinear problems in unbounded domains
No full textAbstractAs formulated by Silva [E.A. de B.e. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Anal. 16 (1991) 455–477] and Schechter [M. Schechter, A generalization of the saddle point method with applications, Ann. Polon. Math. 57 (3) (1992) 269–281; M. Schechter, New saddle point theorems, in: Generalized Functions and Their Applications, Varanasi, 1991, Plenum, New York, 1993, pp. 213–219], the sandwich theorem has become a very useful tool in finding critical points of functionals leading to solutions of partial differential equations. In the present paper, this theorem is strengthened to apply to more general situations. We present some applications
A characterization of the Schechter essential spectrum on Banach spaces and applications
No full textAbstractIn a recent article by the author (C. R. Acad. Sci. Paris Sér. I 331 (2000) 525–530; Boll. Un. Mat. Ital. (2002), to appear) the Schechter spectrum of closed, densely defined linear operators has been characterized on spaces, which possess the Dunford–Pettis property or which are isomorphic to one of the spaces Lp(Ω), p>1. The purpose of the present work is to extend this analysis to the case of Banach spaces. Further we apply the obtained results to investigate the Schechter essential spectrum of one-dimensional transport equations with different boundary conditions
Multiple solutions of second order Hamiltonian systems
No full textThe existence and the multiplicity of periodic solutions for a parameter dependent second order Hamiltonian system are established via linking theorems. A monotonicity trick is adopted in order to prove the existence of an open interval of parameters for which the problem under consideration admits at least two non trivial qualified solutions
Some notes on a superlinear second order Hamiltonian system
No full textVariational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered
doi:10.1155/2007/58948 Research Article The Use of Cerami Sequences in Critical Point Theory
No full textThe concept of linking was developed to produce Palais-Smale (PS) sequencesG(uk) → a, G′(uk) → 0 for C1functionals G that separate linking sets. These sequences produce criti-cal points if they have convergent subsequences (i.e., ifG satisfies the PS condition). In the past, we have shown that PS sequences can be obtained even when linking does not exist. We now show that such situations producemore useful sequences. They not only produce PS sequences, but also Cerami sequences satisfying G(uk) → a, (1 + ||uk||)G′(uk) → 0 as well. A Cerami sequence can produce a critical point even when a PS sequence does not. In this situation, it is no longer necessary to show that G satisfies the PS condition, but only that it satisfies the easier Cerami condition (i.e., that Cerami sequences have conver-gent subsequences). We provide examples and applications. We also give generalizations to situations when the separating criterion is violated. Copyright © 2007 Martin Schechter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1
The spectrum of the Schrödinger operator
No full textWe describe the negative spectrum of the Schrödinger operator with a singular potential. We determine the exact value of the bottom of the spectrum and estimate it from above and below. We describe the dependence of a crucial constant on the eigenvalue parameter and discuss some of its properties. We show how recent results of others are simple consequences of a theorem proved by the author in 1972.</p
Professional writing today: A functional approach
No full textThis textbook provides guidance for writing in professional workplaces. This book is ideal for students at the beginning of their careers and entry-level employees looking to move to the next level.open accessPublished. This PDF is a representation of the book as at October 27, 2022. The online version may have been updated and includes interactive components. For the most recent interactive version, please visit the online book linked in this record.business communication and presentationcommunication
Public relations: From strategy to action
No full textPublic Relations: From Strategy to Action guides students through the process and practice of engaging in the world of public relations. The book teaches audience analysis, campaign planning, strategy, tactics, message development, and media relations for the PR practitioners of today and the future.Published. This PDF is a representation of the book as of June, 2023. The online version may have been updated and includes interactive components. For the most recent interactive version, please visit the online book linked in this record.Public relation
Public speaking for today's audiences
No full textPublic Speaking for Today's Audiences explains the process and craft of creating and delivering impactful speeches, both for in-person and digital audiences. This book was written for CMNS 1125: Public Speaking at Douglas College, but could also be a valuable textbook for many other undergraduate professional writing courses (and CMNS 1125 transfers as equivalent to many other post-secondary institutions, especially in British Columbia). It is ideal for students and professionals looking to build skill and confidence in their current and future professions.Published. This PDF is a representation of the book as at January, 2023. The online version may have been updated and includes interactive components. For the most recent interactive version, please visit the online book linked in this record.communicationbusiness communication and presentatio
- …
