Displaying similar documents to “Exact solutions of generalized Lane-Emden equations of the second kind”

Boundedness results of solutions to the equation x ′′′ + a x ′′ + g ( x ) x + h ( x ) = p ( t ) without the hypothesis h ( x ) sgn x 0 for | x | > R .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ( x ) sgn x 0 f o r | x | > R , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

Positive solutions of a fourth-order differential equation with integral boundary conditions

Seshadev Padhi, John R. Graef (2023)

Mathematica Bohemica

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We study the existence of positive solutions to the fourth-order two-point boundary value problem u ' ' ' ' ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ' ( 0 ) = u ' ( 1 ) = u ' ' ( 0 ) = 0 , u ( 0 ) = α [ u ] , where α [ u ] = 0 1 u ( t ) d A ( t ) is a Riemann-Stieltjes integral with A 0 being a nondecreasing function of bounded variation and f 𝒞 ( [ 0 , 1 ] × + , + ) . The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii’s fixed point theorem and the Avery-Peterson fixed point theorem.

Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew Omonigho Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

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We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results....

E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } induced by A does not degenerate at E 0 , then it degenerates at E 1 . We apply this result to prove the degeneration at E 1 of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of d ' d ' ' -lemma.

On a divisibility problem

Shichun Yang, Florian Luca, Alain Togbé (2019)

Mathematica Bohemica

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Let p 1 , p 2 , be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if k 5 , then ( p k + 1 - 1 ) ! ( 1 2 ( p k + 1 - 1 ) ) ! p k ! , which improves a previous result of the second author.

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

On hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica z x y ′′ = f ( x , y , z , Z x , z y ) sul planiquarto x 0 , y 0 . Qui, f è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza α .

Shifted values of the largest prime factor function and its average value in short intervals

Jean-Marie De Koninck, Imre Kátai (2016)

Colloquium Mathematicae

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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting s q ( n ) stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence ( α s q ( P ( n ) ) ) n is uniformly distributed modulo 1.

Positive solutions for a system of third-order differential equation with multi-point and integral conditions

Rochdi Jebari, Abderrahman Boukricha (2015)

Commentationes Mathematicae Universitatis Carolinae

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This paper concerns the following system of nonlinear third-order boundary value problem: u i ' ' ' ( t ) + f i ( t , u 1 ( t ) , , u n ( t ) , u 1 ' ( t ) , , u n ' ( t ) ) = 0 , 0 < t < 1 , i { 1 , , n } with the following multi-point and integral boundary conditions: u i ( 0 ) = 0 u i ' ( 0 ) = 0 u i ' ( 1 ) = j = 1 p β j , i u i ' ( η j , i ) + 0 1 h i ( u 1 ( s ) , , u n ( s ) ) d s where β j , i > 0 , 0 < η 1 , i < < η p , i < 1 2 , f i : [ 0 , 1 ] × n × n and h i : [ 0 , 1 ] × n are continuous functions for all i { 1 , , n } and j { 1 , , p } . Using Guo-Krasnosel’skii fixed point theorem in cone, we discuss the existence of positive solutions of this problem. We also prove nonexistence of positive solutions and we give some examples to illustrate our results.

Boundedness results of solutions to the equation x ′′′ + a x ′′ + g ( x ) x + h ( x ) = p ( t ) without the hypothesis h ( x ) sgn x 0 f o r | x | > R .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ( x ) sgn x 0 f o r | x | > R , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

Branching problems and 𝔰𝔩 ( 2 , ) -actions

Pavle Pandžić, Petr Somberg (2015)

Archivum Mathematicum

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We study certain 𝔰𝔩 ( 2 , ) -actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs ( 𝔤 , 𝔭 ) , ( 𝔤 ' , 𝔭 ' ) of Lie algebras and their parabolic subalgebras.

The groups of automorphisms of the Witt W n and Virasoro Lie algebras

Vladimir V. Bavula (2016)

Czechoslovak Mathematical Journal

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Let L n = K [ x 1 ± 1 , ... , x n ± 1 ] be a Laurent polynomial algebra over a field K of characteristic zero, W n : = Der K ( L n ) the Lie algebra of K -derivations of the algebra L n , the so-called Witt Lie algebra, and let Vir be the Virasoro Lie algebra which is a 1 -dimensional central extension of the Witt Lie algebra. The Lie algebras W n and Vir are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: Aut Lie ( Vir ) Aut Lie ( W 1 ) { ± 1 } K * , and give a short proof that Aut Lie ( W n ) Aut K - alg ( L n ) GL n ( ) K * n .

Existence of solutions for a coupled system with φ -Laplacian operators and nonlinear coupled boundary conditions

Konan Charles Etienne Goli, Assohoun Adjé (2017)

Communications in Mathematics

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We study the existence of solutions of the system ( φ 1 ( u 1 ' ( t ) ) ) ' = f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , ( φ 2 ( u 2 ' ( t ) ) ) ' = f 2 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , submitted to nonlinear coupled boundary conditions on [ 0 , T ] where φ 1 , φ 2 : ( - a , a ) , with 0 < a < + , are two increasing homeomorphisms such that φ 1 ( 0 ) = φ 2 ( 0 ) = 0 , and f i : [ 0 , T ] × 4 , i { 1 , 2 } are two L 1 -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

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We consider elementary operators x j = 1 n a j x b j , acting on a unital Banach algebra, where a j and b j are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families a j and b j , i.e. a j = a j ' + i a j ' ' ( b j = b j ' + i b j ' ' ), where all a j ' and a j ' ' ( b j ' and b j ' ' ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...