School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
Abstract
In this paper, we investigate the existence of positive solutions for the eigenvalue problem of nonlinear fractional differential equation with p-Laplacian operator D 0+( p(D 0+u(t))) = f(u(t)), 0 1, −1 p = q, 1/p + 1/q = 1, > 0 is a parameter, and f : (0,+1) ! (0,+1) is continuous. By using the properties of the Green function and the Guo–Krasnosel’skii fixed-point theorem on cones, several new existence results of at least one or two positive solutions in terms of different eigenvalue interval are obtained. Moreover, the nonexistence of positive solution in term of the parameter is also considered.
Lu,H , Han,Z , Sun,S and Zhang,C . (2015). Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian. Scientia Iranica, 22(3), 755-764.
MLA
Lu,H , , Han,Z , , Sun,S , and Zhang,C . "Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian", Scientia Iranica, 22, 3, 2015, 755-764.
HARVARD
Lu H, Han Z, Sun S, Zhang C. (2015). 'Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian', Scientia Iranica, 22(3), pp. 755-764.
CHICAGO
H Lu, Z Han, S Sun and C Zhang, "Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian," Scientia Iranica, 22 3 (2015): 755-764,
VANCOUVER
Lu H, Han Z, Sun S, Zhang C. Positive solutions for eigenvalue problems of fractional differential equation with p-Laplacian. Scientia Iranica. 2015;22(3):755-764.
