Displaying similar documents to “The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations”

Existence Principles for Singular Vector Nonlocal Boundary Value Problems with φ -Laplacian and their Applications

Staněk, Svatoslav (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Existence principles for solutions of singular differential systems ( φ ( u ' ) ) ' = f ( t , u , u ' ) satisfying nonlocal boundary conditions are stated. Here φ is a homeomorphism ℝ N onto ℝ N and the Carathéodory function f may have singularities in its space variables. Applications of the existence principles are given.

Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities

Irena Rachůnková, Svatoslav Staněk (2013)

Open Mathematics

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The paper investigates the structure and properties of the set S of all positive solutions to the singular Dirichlet boundary value problem u″(t) + au′(t)/t − au(t)/t 2 = f(t, u(t),u′(t)), u(0) = 0, u(T) = 0. Here a ∈ (−∞,−1) and f satisfies the local Carathéodory conditions on [0,T]×D, where D = [0,∞)×ℝ. It is shown that S c = {u ∈ S: u′(T) = −c} is nonempty and compact for each c ≥ 0 and S = ∪c≥0 S c. The uniqueness of the problem is discussed. Having a special case of the problem,...

On a two-point boundary value problem for second order singular equations

Alexander Lomtatidze, P. Torres (2003)

Czechoslovak Mathematical Journal

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The problem on the existence of a positive in the interval ] a , b [ solution of the boundary value problem u ' ' = f ( t , u ) + g ( t , u ) u ' ; u ( a + ) = 0 , u ( b - ) = 0 is considered, where the functions f and g ] a , b [ × ] 0 , + ∞ [ → ℝ satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b ) and in the phase variable (for u = 0 ) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.