Existence of Nontrivial Solutions for Fractional Differential Equations with p-Laplacian. (1st January 2019) - Zhang, Li; Wang, Fanglei; Ru, Yuanfang
Abstract : Combining the properties of the Green function with some point theorems, we consider the existence of nontrivial solutions for fractional equations withp -Laplacian operatorD 0 + β ϕ p [ D 0 + α ( p t u ′ ( t ) ) ] + f ( t, u ( t ) ) = 0,     0 < t < 1, a u ( 0 ) - b p 0 u ′ ( 0 ) = 0, andc u ( 1 ) + d p 1 u ′ ( 1 ) = 0, D 0 + α p t u ′ t t = 0 = 0, wherea, b, c, d are constants andp ( · ) : [ 0, 1 ] → ( 0, + ∞ ) is continuous.