Abstract
In this article, together with Leggett–Williams and Guo–Krasnosel’skii fixed point theorems, height functions on special bounded sets are constructed to obtain the existence of at least three positive solutions for some higher-order fractional differential equations with p-Laplacian. The nonlinearity permits singularities both on the time and the space variables, and it also may change its sign.
Highlights
We are devoted to investigating the existence of multiple positive solutions for the following fractional differential equation with p-Laplacian (FPDE for short):
When f is semipositone, Luca [31] investigated the existence of positive solutions for the following fractional differential equations: D0α+u(t) + f t, u(t) = 0, 0 < t < 1, (2)
Motivated by papers mentioned above and the multiple solutions results such as in [3,4,5, 28], the purpose of this paper is to investigate the existence of at least triple positive solutions for FPDE (1)
Summary
We are devoted to investigating the existence of multiple positive solutions for the following fractional differential equation with p-Laplacian (FPDE for short):. By constructing height functions in different bounded sets, researchers obtained existence results on positive solutions and multiple positive solutions for some fractional nonlocal problems [31,33,34,46,51]. When f is semipositone, Luca [31] investigated the existence of positive solutions for the following fractional differential equations: D0α+u(t) + f t, u(t) = 0, 0 < t < 1,. As far as we know, there are relatively few results on multiple solutions for fractional differential equation nonlocal problems when the nonlinearity permits singularities both on the time and the space variables. This makes the verification of the condition easier and more efficient
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