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  • 1
    Language: English
    In: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2015, Vol.117(2), pp.161-164
    Subject(s): Mathematics ; Mathematics, General ; Mathematics;
    ISSN: 0012-0456
    E-ISSN: 1869-7135
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  • 2
    Language: English
    In: Boundary Value Problems, 2013, Vol.2013(1), pp.1-10
    Description: The aim of this article is to describe some fundamental contributions of Jean Mawhin to critical point theory and its applications to boundary value problems.
    Subject(s): Mathematics;
    E-ISSN: 1687-2770
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  • 3
    Article
    Article
    2014
    ISSN: 0032-5155 
    Language: English
    In: Portugaliae Mathematica, 2014, Vol.71(3), pp.177-182
    Description: We use some isoperimetric constants in order estimate the best constants in some Sobolev inequalities.
    Subject(s): Real Functions ; Isoperimetric Inequalities ; Sobolev Inequalities ; Poincaré-Sobolev Inequalities ; Cheeger Inequality ; Coarea Formula ; Mathematics
    ISSN: 0032-5155
    E-ISSN: 1662-2758
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  • 4
    Article
    Article
    2014
    ISSN: 0021-7670 
    Language: English
    In: Journal d'Analyse Mathématique, 2014, Vol.122(1), pp.69-85
    Description: We consider partial symmetry of the least energy solutions of some nonlinear Schrödinger systems. We show that in the attractive case, all components of the least energy solutions possess foliated Schwarz symmetry with respect to the same point.
    Subject(s): Mathematics ; Analysis ; Functional Analysis ; Dynamical Systems and Ergodic Theory ; Abstract Harmonic Analysis ; Partial Differential Equations ; Applied Sciences ; Mathematics;
    ISSN: 0021-7670
    E-ISSN: 1565-8538
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  • 5
    Language: English
    In: Journal of Fixed Point Theory and Applications, 2010, Vol.7(2), pp.265-290
    Description: In 1963–64, Palais and Smale have introduced a compactness condition, namely condition (C), on real functions of class C 1 defined on a Riemannian manifold modeled upon a Hilbert space, in order to extend Morse theory to this frame and study nonlinear partial differential equations. This condition and some of its variants have been essential in the development of critical point theory on Banach spaces or Banach manifolds, and are referred as Palais–Smale-type conditions. The paper describes their evolution.
    Subject(s): 58E05 ; 58-03 ; 01A60
    ISSN: 1661-7738
    E-ISSN: 1661-7746
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  • 6
    Article
    Article
    2006
    ISSN: 13701444 
    In: Bulletin of the Belgian Mathematical Society - Simon Stevin, July 2006, Vol.13(3), pp.435-440
    Description: We give simple proofs of the representation theorems of Riesz and Schwartz.
    Subject(s): Bounded Variation ; Distribution Theory ; Measure Theory ; Representation Theorem ; Stieltjes Integral
    ISSN: 13701444
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  • 7
    Language: English
    In: 2018
    Description: We consider the forced problem$-\Delta_p u - V(x)|u|^{p-2} u = f(x)$,where $\Delta_p$ is the $p$-Laplacian ($1〈p〈\infty$) in a domain $\Omega\subset \mathbb{R}^N$, $V\ge 0$ and$Q_V (u) := \int_\Omega |\nabla u|^p\, dx - \int_\Omega V|u|^p\,dx$ satisfies the condition (A) below. We show that this problem has a solution for all $f$ in a suitable space of distributions. Then we apply this result to some classes of functions $V$ which in particular include the Hardy potential \eqref{hardy2} and the potential $V(x)=\lambda_{1,p}(\Omega)$, where $\lambda_{1,p}(\Omega)$ is the Poincar\'e constant on an infinite strip.
    Subject(s): Natural Sciences ; Mathematics ; Naturvetenskap ; Matematik ; Forced Problem ; Hardy Potential ; P-Laplacian ; Poincaré Constant ; Weakly Coercive ; Matematik ; Mathematics
    Source: SwePub (National Library of Sweden)
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  • 8
    Article
    Article
    1981
    ISSN: 0002-9939 
    Language: English
    In: Proceedings of the American Mathematical Society, 1981, Vol.83, pp.341-344
    Description: Let $ L$ and let $ \psi $. Under a nonresonance assumption, we prove that the range of $ L + \partial \psi $.
    Subject(s): Semilinear Equations ; Nonconvex Duality
    ISSN: 0002-9939
    E-ISSN: 1088-6826
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  • 9
    Language: English
    In: Proceedings of the American Mathematical Society, 1995, Vol.123, pp.3555-3561
    Description: We study the semilinear elliptic equation $ - \Delta u = \lambda \vert u{\vert^{q - 2}}u + \mu \vert u{\vert^{p - 2}}u$ $ \Omega \subset {\mathbb{R}^N}$ $ 1 〈 q 〈 2 〈 p 〈 {2^ \ast }$ 0$ --〉 $ \lambda 〉 0$ $ \mu \in \mathbb{R}$ of solutions with negative energy converging to 0 as $ k \to \infty $ and arbitrary there exists a sequence of solutions with unbounded energy. This answers a question of Ambrosetti, Brézis and Cerami. The main ingredient is a new critical point theorem, which guarantees the existence of infinitely many critical values of an even functional in a bounded range. We can also treat strongly indefinite functionals and obtain similar results for first-order Hamiltonian systems.
    Subject(s): Mathematics -- Mathematical values -- Critical values ; Mathematics -- Mathematical expressions -- Mathematical theorems ; Mathematics -- Mathematical expressions -- Equations ; Mathematics -- Mathematical values -- Critical values ; Mathematics -- Logic -- Logical topics ; Philosophy -- Applied philosophy -- Social philosophy ; Philosophy -- Mathematical objects -- Mathematical sequences ; Mathematics -- Mathematical objects -- Mathematical sequences;
    ISSN: 0002-9939
    E-ISSN: 1088-6826
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  • 10
    Language: English
    In: World Journal of Surgery, 2012, Vol.36(12), pp.2872-2878
    Description: Byline: Zohra Faiz (1), Valery E. P. P. Lemmens (2,3), Peter D. Siersema (4), Grard A. P. Nieuwenhuijzen (5), Michel W. J. M. Wouters (6), Tom Rozema (7), Jan Willem W. Coebergh (1,2), Bas P. L. Wijnhoven (1) Abstract: Background The incidence of esophageal cancer has grown over the recent decades and 30 % of esophageal cancer patients are now 75 years or older at the time of diagnosis. The aim of this study was to evaluate trends in management and survival of patients aged 75 years or older with esophageal cancer. Methods In the Netherlands cancer registry, we identified all patients aged 75 years or older who were diagnosed with esophageal cancer between 1989 and 2008. Trends in management and survival were analyzed by time period (1989--2001 vs. 2002--2008), TNM stage, and age (75--79, 80--84, and 85+ years). [chi].sup.2 testing was used to analyze time trends in treatment, Kaplan--Meier analysis and log-rank testing to estimate survival, and Cox regression model to calculate hazard ratios for death. Results Some 7,253 patients were included in the study. The surgical resection rate increased over the 1989--2008 period from 8.9 to 12.6 % (p = 0.028), especially among patients aged 75--79 years (44.6 vs. 55.4 %, p 〈 0.001) and patients with TNM stage I disease (12.7 vs. 22.0 %, p 〈 0.001). The use of definitive chemoradiotherapy (CRT) also increased (0.19 vs. 2.20 %, p 〈 0.001). Whereas the use of chemotherapy as a single-modality treatment more than doubled (0.64 vs. 1.54 %, p = 0.004), that of radiotherapy alone decreased (38.1 vs. 31.6 %, p 〈 0.001). Although median survival time was marginally higher in the 2002--2008 period than in 1989--2001, overall 5 year survival rates remained low at 6 and 5 %, respectively (p 〈 0.001). Five-year survival rate after surgery increased from 16 to 30 % (p 〈 0.001). Conclusions In patients of 75 years or older, surgical treatment and use of definitive CRT have increased between 1989 and 2008. Also, an increase in the use of chemotherapy as a single modality was noted. Overall 5 year survival for all cancer patients was stable but remained poor, while survival of patients who underwent esophagectomy improved significantly in the Netherlands since 1989. Author Affiliation: (1) Department of Surgery, Erasmus MC, P.O. Box 2040, 3000 CA, Rotterdam, The Netherlands (2) Department of Research, Eindhoven Cancer Registry, Comprehensive Cancer Centre South, Eindhoven, The Netherlands (3) Department of Public Health, Erasmus MC, Rotterdam, The Netherlands (4) Department of Gastroenterology and Hepatology, University Medical Center, Utrecht, The Netherlands (5) Department of Surgery, Catharina Hospital, Eindhoven, The Netherlands (6) Department of Surgery, Netherlands Cancer Institute, Amsterdam, The Netherlands (7) Department of Radiotherapy, Verbeeten Institute, Tilburg, The Netherlands Article History: Registration Date: 10/08/2012 Online Date: 11/09/2012
    Subject(s): Surgery -- Analysis ; Surgery -- Statistics ; Cancer Research -- Analysis ; Cancer Research -- Statistics ; Esophageal Cancer -- Patient Outcomes ; Esophageal Cancer -- Analysis ; Esophageal Cancer -- Statistics ; Public Health -- Analysis ; Public Health -- Statistics ; Chemotherapy -- Analysis ; Chemotherapy -- Statistics;
    ISSN: 0364-2313
    E-ISSN: 1432-2323
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