Displaying similar documents to “Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation”

The existence of a periodic solution of a parabolic equation with the Bessel operator

Dana Lauerová (1984)

Aplikace matematiky

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In this paper, the existence of an ω -periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions f ( t , r ) , h ( t ) , a ( t ) are assumed to be ω -periodic in t , f ∈ L 2 ( S , H ) , a , h such that a ' ∈ L ∞ ( R ) , h ' ∈ L ∞ ( R ) and they fulfil (3). The solution u belongs to the space L 2 ( S , V ) ∩ L ∞ ( S , H ) , has the derivative u ' ∈ L 2 ( S , H ) and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.

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 ⁴ 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 .

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 : ℝ × ℝ 2 n + 1 → ℝ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity f ( t , x ₀ , x ₁ , . . . , 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].

Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

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In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form b ( u ) , where b ∈ L loc ∞ ( R ) . Extending b to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

Abstract inclusions in Banach spaces with boundary conditions of periodic type

Lahcene Guedda, Ahmed Hallouz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ x ∈ S ( x ( 0 ) , s e l F ( x ) ) ⎨ ⎩ x (T) = x(0), where, F : [ 0 , T ] × → 2 E is a multivalued map with convex compact values, ⊂ E, s e l F is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed...