Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian

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.

[1]  Lishan Liu,et al.  The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems , 2016 .

[2]  Alberto Cabada,et al.  Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations , 2012, Appl. Math. Lett..

[3]  Ying Wang,et al.  Uniqueness and existence of positive solutions for the fractional integro-differential equation , 2017 .

[4]  E. Kaufmann,et al.  Positive solutions of a boundary value problem for a nonlinear fractional differential equation. , 2008 .

[5]  D. O’Regan,et al.  On the existence of two nontrivial solutions of periodic problems with operators of p-Laplacian type , 2007 .

[6]  Hongjun Xiang,et al.  Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations , 2010 .

[7]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[8]  Lishan Liu,et al.  Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces , 2017 .

[9]  Wengui Yang,et al.  Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions , 2012, Comput. Math. Appl..

[10]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[11]  Y. Wang,et al.  Positive solutions of periodic boundary value problems for the second-order differential equation with a parameter , 2017, Boundary Value Problems.

[12]  Yonghong Wu,et al.  The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition , 2014, Appl. Math. Comput..

[13]  Lishan Liu,et al.  Positive solutions for nonlinear fractional semipositone differential equation with nonlocal boundary conditions , 2016 .

[14]  N. Mahmudov,et al.  Existence of solutions of fractional boundary value problems with p-Laplacian operator , 2015, Boundary Value Problems.

[15]  Haiyan Wang,et al.  On the number of positive solutions of nonlinear systems , 2003 .

[16]  Christopher S. Goodrich,et al.  Existence of a positive solution to systems of differential equations of fractional order , 2011, Comput. Math. Appl..

[17]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[18]  Xinguang Zhang,et al.  Positive Solutions for (n - 1, 1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions , 2014 .

[19]  Johnny Henderson,et al.  Positive solutions for a system of fractional differential equations with coupled integral boundary conditions , 2014, Appl. Math. Comput..

[20]  Lishan Liu,et al.  Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters , 2014 .

[21]  Johnny Henderson,et al.  Positive solutions for a system of nonlocal fractional boundary value problems , 2013 .

[22]  Xinguang Zhang,et al.  Spectral Analysis for a Singular Differential System with Integral Boundary Conditions , 2016 .

[23]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[24]  Hongling Lu,et al.  Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p-Laplacian , 2013, Advances in Difference Equations.