Abstract
In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.
Highlights
We study the existence, nonexistence and multiplicity of positive solutions to the following problem
For sign-changing weight h satisfying |h| ∈ H φ and c ≡ d ≡ 1, Xu [20] studied the existence of a nontrivial solution to problem (1) for all small λ > 0 under the assumptions that f ∈ C (R, R) is non-decreasing, f (0) > 0 and f ∞ ∈ (0, ∞)
We studied the existence and nonexistence of positive solutions to problem (1)
Summary
We study the existence, nonexistence and multiplicity of positive solutions to the following problem For sign-changing weight h satisfying |h| ∈ H φ and c ≡ d ≡ 1, Xu [20] studied the existence of a nontrivial solution to problem (1) for all small λ > 0 under the assumptions that f ∈ C (R, R) is non-decreasing, f (0) > 0 and f ∞ ∈ (0, ∞). In order to overcome this difficulty, a lemma ([2], Lemma 2.4) was proved, so that various results for the existence, nonexistence and multiplicity of positive solutions to problem (1) were proved in Reference [2] when d is non-decreasing on [0, 1] and h ∈ C [0, 1] satisfies h 6≡ 0 on any subinterval of [0, 1].
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