Abstract
In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on the existence and nonexistence of positive solutions is also investigated. An example is then given to illuminate the application of the main results.
Highlights
By the properties of Green’s function and the Guo-Krasnosel’skii fixed point theorem, some results on the existence of positive solutions are obtained
In this paper, our main research is the existence and nonexistence of positive solutions for the following fractional coupled system with generalized p-Laplacian involving RiemannStieltjes integral conditions. ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨DDβ β ++(φ (φ (Dα + (Dα + u(t))) v(t))) + +λ f (t, λ f (t, u(t), u(t), v(t)) v(t)) = = < t
2 Preliminaries and lemmas For convenience of the reader, we present some necessary definitions about fractional calculus theory
Summary
By the properties of Green’s function and the Guo-Krasnosel’skii fixed point theorem, some results on the existence of positive solutions are obtained. By the Guo-Krasnosel’skii fixed point theorem, the authors in [ ] got the existence of positive solutions on system ( ).
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