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Positive and maximal positive solutions of singular mixed boundary value problem

100%
Agarwal R., O’Regan D., Staněk S.
Open Mathematics
|
2009
|
tom 7
|
nr 4
694-716
EN
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.
2
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Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities

76%
Rachůnková I., Staněk S.
Open Mathematics
|
2013
|
tom 11
|
nr 1
112-132
EN
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, we introduce an ordering in S showing that the difference of any two solutions in S c,c≥ 0, keeps its sign on [0,T]. An application to the equation v″(t) + kv′(t)/t = ψ(t)+g(t, v(t)), k ∈ (1,∞), is given.
3
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Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

64%
Jessada T., Ntouyas S. K., Asawasamrit S., Promsakon C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
645-666
EN
In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.
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