Abstract
In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. Under different combinations of superlinearity and sublinearity of the nonlinearities, various existence results for positive solutions are derived in terms of different values of parameters via the Guo-Krasnosel’skii fixed point theorem.
Highlights
1 Introduction In this paper, we investigate the following system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator:
By means of the Avery-Henderson fixed point theorem and six functionals fixed point theorem, Rao [26] investigated the existence of multiple positive solutions for a coupled system of p-Laplacian fractional order two point boundary value problems
Motivated by the papers mentioned above, in this paper, we study the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator
Summary
We investigate the following system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator:. Xu and Dong [17] considered the following three point boundary value problem of fractional differential equation with p-Laplacian operator:. Lv [20] discussed an m-point boundary value problem of fractional differential equation with p-Laplacian operator. By means of the Avery-Henderson fixed point theorem and six functionals fixed point theorem, Rao [26] investigated the existence of multiple positive solutions for a coupled system of p-Laplacian fractional order two point boundary value problems. Motivated by the papers mentioned above, in this paper, we study the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. For any (u, v) ∈ P ∩ ∂ 2, by the definitions of f ∗ and g∗, we have f t, u(t), v(t) ≤ f ∗ t, (u, v) Y , g t, u(t), v(t) ≤ g∗ t, (u, v) Y , t ∈ [0, 1], so
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