Multiple positive solutions for a fourth-order p-Laplacian Sturm-Liouville boundary value problems on time scales

Abstract

In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scaleswhere φp(s) is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.

Positive solutions to fractional boundary-value problems with p-Laplacian on time scales

“…For α = 2, problem (1.1), (1.2) is called a fourth order p-Laplacian boundary-value problem which has been studied in [4]. Dong et al [22] investigated the boundary-value problem for a fractional differential equation with the p-Laplacian operator Motivated by the work mentioned above, we investigate the existence and multiplicity of positive solutions for (1.3), (1.4) on time scales.…”

“…Due to the wide applications, many researchers studied the existence of positive solutions for fractional derivatives boundaryvalue problem [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein. Meanwhile, the boundary-value problem with p-Laplacian operator have also been discussed extensively in the literature; for example, see [4,11,[22][23][24][25][26][27].…”