Abstract
This paper deals with the existence of triple positive solutions for a type of second-order singular boundary problems with general differential operators. By using the Leggett-Williams fixed point theorem, we establish an existence criterion for at least three positive solutions with suitable growth conditions imposed on the nonlinear term.
Highlights
We study the existence of triple positive solutions for the following second-order singular boundary value problems with general differential operators: utatutbtuthtft, u t 0, t ∈ 0, 1, 1.1 u 0 u 1 0, where a ∈ C 0, 1 ∩ L1 0, 1, b ∈ C 0, 1, −∞, 0, and h ∈ C 0, 1, 0, ∞ with t 1 − t |b t |dt < ∞, t 1 − t h t dt < ∞
The Leggett-William fixed point theorem is used extensively in the study of triple positive differential equations, the method has not been used to study this type of second-order singular boundary value problem with general differential operators
Lemma 2.1of 2 together with the facts that φ ∈ C1 0, 1 and H3 implies that limφ t 1 − s h s ds 0
Summary
We study the existence of triple positive solutions for the following second-order singular boundary value problems with general differential operators: utatutbtuthtft, u t 0, t ∈ 0, 1 , 1.1 u 0 u 1 0, where a ∈ C 0, 1 ∩ L1 0, 1 , b ∈ C 0, 1 , −∞, 0 , and h ∈ C 0, 1 , 0, ∞ with t 1 − t |b t |dt < ∞, t 1 − t h t dt < ∞. The Leggett-William fixed point theorem is used extensively in the study of triple positive differential equations, the method has not been used to study this type of second-order singular boundary value problem with general differential operators.
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