Displaying similar documents to “Stable periodic solutions in scalar periodic differential delay equations”

Positive periodic solutions of a neutral functional differential equation with multiple delays

Yongxiang Li, Ailan Liu (2018)

Mathematica Bohemica

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This paper deals with the existence of positive ω -periodic solutions for the neutral functional differential equation with multiple delays ( u ( t ) - c u ( t - δ ) ) ' + a ( t ) u ( t ) = f ( t , u ( t - τ 1 ) , , u ( t - τ n ) ) . The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of c and the coefficient function a ( t ) , and the nonlinearity f ( t , x 1 , , x n ) . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Commentationes Mathematicae Universitatis Carolinae

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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay x ' ( t ) = - t - τ ( t ) t a ( t , s ) g ( x ( s ) ) d s + d d t Q ( t , x ( t - τ ( t ) ) ) + G ( t , x ( t ) , x ( t - τ ( t ) ) ) . We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for τ , g , a , Q and G to show that this sum of mappings fits into the framework of a modification of...

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

Yongxiang Li, He Yang (2011)

Annales Polonici Mathematici

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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation u ( 2 n + 1 ) = f ( t , u , u ' , . . . , u ( 2 n ) ) , where f : × 2 n + 1 is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity f ( t , x , x , . . . , x 2 n ) to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].

Generalized c -almost periodic type functions in n

M. Kostić (2021)

Archivum Mathematicum

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In this paper, we analyze multi-dimensional quasi-asymptotically c -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl c -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically c -almost periodic functions and reconsider the notion of semi- c -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...

Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li, Changzhao Li, Juan Zhang (2010)

Annales Polonici Mathematici

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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), t t j , j ∈ ℤ, ⎨ ⎩ y ( t j ) = y ( t ¯ j ) + I j ( y ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × n is a nonsingular matrix with continuous real-valued entries.

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

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Let a , . . . , a k be arbitrary nonzero real numbers. An ( a , . . . , a k ) -decomposition of a function f:ℝ → ℝ is a sum f + + f k = f where f i : is an a i -periodic function. Such a decomposition is not unique because there are several solutions of the equation h + + h k = 0 with h i : a i -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the ( a , . . . , a k ) -decomposition is essentially unique. We characterize those periods for which essential...

Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Lingbin Kong, Daqing Jiang (1998)

Annales Polonici Mathematici

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The fourth order periodic boundary value problem u ( 4 ) - m u + F ( t , u ) = 0 , 0 < t < 2π, with u ( i ) ( 0 ) = u ( i ) ( 2 π ) , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of ± 10 - 7 .

The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian

Jean Mawhin (2006)

Journal of the European Mathematical Society

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We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation ( | u ' | p 2 u ' ) ) ' + f ( u ) u ' + g ( x , u ) = t , when f is arbitrary and g ( x , u ) + or g ( x , u ) when | u | . The proof uses upper and lower solutions and the Leray–Schauder degree.

Remotely c -almost periodic type functions in n

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely c -almost periodic functions in n , slowly oscillating functions in n , and further analyze the recently introduced class of quasi-asymptotically c -almost periodic...

Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas

Hans-Otto Walther

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CONTENTSIntroduction...........................................................................................................................................5  I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family...