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8172. Existence results for a fourth order partial differential equation arising in condensed matter physics
- Creator:
- Escudero, Carlos, Gazzola, Filippo, Hakl, Robert, Peral, Ireneo, and Torres, Pedro José
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- higher order parabolic equation, existence of solution, blow-up in finite time, higher order elliptic equation, variational method, and strongly singular boundary value problem
- Language:
- English
- Description:
- We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8173. Existence results for systems with nonlinear coupled nonlocal initial conditions
- Creator:
- Bolojan, Octavia, Infante, Gennaro, and Precup, Radu
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- nonlinear differential system, nonlocal boundary condition, nonlinear boundary condition, fixed point, vector-valued norm, and matrix convergent to zero
- Language:
- English
- Description:
- The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are given to illustrate the theory.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8174. Existence results of positive solutions to fractional differential equation with integral boundary conditions
- Creator:
- Zhang, Shuqin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- fractional differential equation, integral boundary conditions, positive solutions, fixed point index, and cone
- Language:
- English
- Description:
- In this paper we consider the existence, multiplicity, and nonexistence of positive solutions to fractional differential equation with integral boundary conditions. Our analysis relies on the fixed point index.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8175. Existence theorems for nonlinear differential equations having trichotomy in Banach spaces
- Creator:
- Gomaa, Adel Mahmoud
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, nonlinear differential equation, trichotomy, existence theorem, 13, and 51
- Language:
- English
- Description:
- We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation x(t)=L(t)x(t)+f(t,x(t)), t R where {L(t) in R}$ is a family of linear operators from a Banach space E into itself and f R E to E. By L(E) we denote the space of linear operators from E into itself. Furthermore, for a<b and d>0, we let C([-d,0],E) be the Banach space of continuous functions from [-d,0] into E and f^d [a,b] C([-d,0],E) E. Let L: [a,b] to L(E) be a strongly measurable and Bochner integrable operator on [a,b] and for t in [a,b] define tau_tx(s)=x(t+s) for each s in[-d,0]. We prove that, under certain conditions, the differential equation with delay x(t)=L(t)x(t)+f^d(t,tau_tx) if t in [a,b], Q has at least one weak solution and, under suitable assumptions, the differential equation (Q) has a solution. Next, under a generalization of the compactness assumptions, we show that the problem (Q) has a solution too., Adel Mahmoud Gomaa., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8176. Existence, uniqueness and global asymptotic stability for a class of complex-valued neutral-type neural networks with time delays
- Creator:
- Tan, Manchun and Xu, Desheng
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- complex-valued neutral-type neural networks, existence and uniqueness of equilibrium, global asymptotic stability, inequality techniques, Lyapunov functional, and Lyapunov functional
- Language:
- English
- Description:
- This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium point for complex-valued neutral-type neural networks are obtained. Finally, numerical examples are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8177. Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $\Bbb R^n$
- Creator:
- Farwig, Reinhard and Sohr, Hermann
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- stationary Stokes and Navier-Stokes system, very weak solutions;, existence and uniqueness in higher dimensions, and regularity classes in higher dimensions
- Language:
- English
- Description:
- For a bounded domain $\Omega \subset \Bbb R ^n$, $n\geq 3,$ we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system $-\Delta u + u \cdot \nabla u + \nabla p=f$, $\div u = k$, $u_{|_{\partial \Omega }}=g$ with $u \in L^q$, $q \geq n$, and very general data classes for $f$, $k$, $g$ such that $u$ may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžička, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669--717, where the existence of a weak solution which is locally regular is proved.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8178. Existenciální racionalismus Karla Jasperse
- Creator:
- Bojda, Martin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Karl Jaspers, filosofie existence, racionalismus, německá filosofie, idealismus, komunikace, láska, philosophy of existence, rationalism, German philosophy, idealism, communication, love, Existenzphilosophie, Rationalismus, deutsche Philosophie, Idealismus, Kommunikation, and Liebe
- Language:
- Czech
- Description:
- Karl Jaspers proslul v meziválečné době jako zakladatel nové filosofie existence, která však byla v kombinaci s jeho psychologickým školením, zaostřením na ,,mezní situace“ lidského prožívání a kritikou filosofických systémů často dezinterpretována jako forma subjektivismu či iracionalismu. Předložená studie se pokouší vystihnout jádro Jaspersova využití filosofie existence pro novou rekonstrukci lidské racionality, univerzálních charakteristik lidství. Jejich pochopení mělo podle Jasperse vzdorovat pokořování lidské důstojnosti v moderních totalitách a v globálním ekonomicko-technologickém provozu, pro něž hodnoty lidství, jak je definuje Jaspersova filosofie, přestaly být určujícími měřítky. Studie ukazuje Jaspersovo ukotvení existence ve vztahu k transcendenci a individuality v komunikaci s druhým a jeho kritiku monistického myšlení, které pluralitu ve smyslu jeho filosofické koncepce neumožňuje., Karl Jaspers received much attention in the interwar period as the founder of a new philosophy of existence that, however, was – in tandem with his psychological training, focus on “borderline situations” of human experience, and critique of philosophical systems – often misinterpreted as a form of subjectivism or irrationalism. The study presented here strives to depict the substance of Jaspers’ use of the philosophy of existence for a new reconstruction of human rationality, of the universal characteristics of humanity. Understanding these characteristics shall, in his estimation, help us to resist the degradation of human dignity in modern totalitarianism and in the global economic-technological system, in which the values of humanity, as defined by Jaspers’ philosophy, have ceased being decisive criteria. The study presents Jaspers’ anchoring of existence in the relationship to transcendence and of individuality in the communication with others, as well as his critique of monistic thinking, which in his philosophical conception does not allow for plurality., and Karl Jaspers wurde in der Zwischenkriegszeit als Begründer der Existenzphilosophie bekannt, die jedoch im Zusammenhang mit der psychologischen Ausbildung Jaspers’, der Konzentration auf „Grenzsituationen“ des menschlichen Erlebens und der Kritik philosophischer Systeme oft als eine Form von Subjektivismus bzw. Irrationalismus fehlinterpretiert wurde. In der vorliegenden Studie wird der Versuch unternommen, den Kern von Jaspers’ Nutzung der Existenzphilosophie für eine Rekonstruktion der menschlichen Rationalität und der universalen Merkmale des Menschseins zu erfassen. Deren Erkenntnis sollte laut Jaspers der Demütigung der Menschenwürde in modernen totalitären Regimen und im globalen ökonomisch-technologischen Betrieb widerstehen, in denen die in Jaspers’ Philosophie definierten Werte des Menschseins kein Maßstab mehr sind. In der Studie wird Jaspers’ Verankerung der Existenz in der Beziehung zur Transzendenz und zur Individualität in der Kommunikation mit anderen und seine Kritik am monistischen Denken aufgezeigt, das keine Pluralität im Sinne seines philosophischen Konzepts ermöglicht.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8179. Existuje lidský gen homosexuality?
- Creator:
- Wernerová, Markéta, Olivová, Jana, Svoboda, Luděk , and Pačes, Jan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Language:
- Czech
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8180. Existuje mentální kognitivní technologie?
- Creator:
- Fajkus, Břetislav
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- physics, mental phenomena, cognitive technology, and philosophy of science
- Language:
- Slovak
- Description:
- In his book Physics of the Impossible, Michio Kaku thinks that psycho-kinesis-i.e., a direct causal influence on physical processes by mental powers-will become a real possibility in a near future. From the point of view of metaphysical realism, this means that mental entities and mental causality are real phenomena. Contemporary scientific methodology regards the use of scientific instruments that amplify our sensibilities as a cognitive technology that deepens our knowledge of, and power over, real processes. It appears that the strongest and most productive methods are connected with scientific theories-they are theories ''in action''. Thus, scientific theories can regarded as mental cognitive technology by means of which humans get to know, and at the same time shape, reality. and Břetislav Fajkus
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public