Existence of Triple Positive Solutions of a Kind of Second-order Four-point BVP

다국어 초록 (Multilingual Abstract)

In this paper, we considered the following four-point boundary
value problem
x“(t) + h(t)f(t,x(t), x‘(t)) = 0, 0 < t < 1
x‘(0) = ax<기호>, x’(1) = bx(η),
where 0 <<기호> <η < 1, <기호>= ab<기호>- abη+a−b > 0, 0 < a <<기호>
, 0 <b <<기호>
. After the discussion of the Green function of the corresponding
homogeneous system, we establish some criteria for the existence of positive
solutions by using the generalized Leggett-William’'s fixed point theorem.
The interesting point is the expression of the Green function, which is a
difficulty for multi-point BVP.

다국어 초록 (Multilingual Abstract)

In this paper, we considered the following four-point boundary
value problem
x“(t) + h(t)f(t,x(t), x‘(t)) = 0, 0 < t < 1
x‘(0) = ax<기호>, x’(1) = bx(η),
where 0 <<기호> <η < 1, <기호>= ab<기호>- abη+a−b > 0, 0 < a <<기호>
, 0 <b <<기호>
. After the discussion of the Green function of the corresponding
homogeneous system, we establish some criteria for the existence of positive
solutions by using the generalized Leggett-William’'s fixed point theorem.
The interesting point is the expression of the Green function, which is a
difficulty for multi-point BVP.

참고문헌 (Reference)

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