Displaying similar documents to “Periodic boundary value problems for second-order functional differential equations.”

Periodic solutions for third order ordinary differential equations

Juan J. Nieto (1991)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.

Fractional BVPs with strong time singularities and the limit properties of their solutions

Svatoslav Staněk (2014)

Open Mathematics

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In the first part, we investigate the singular BVP d d t c D α u + ( a / t ) c D α u = ℋ u , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where ℋ is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems d d t c D α n u + ( a / t ) c D α n u = f ( t , u , c D β n u ) , u(0) = A, u(1) = B, c D α n u ( t ) t = 0 = 0 where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t,...