Multiplicity of Positive Solutions for Fractional Differential Equation with p -Laplacian Boundary Value Problems

Abstract EN

We investigate the existence of multiple positive solutions of fractional differential equations with p -Laplacian operator D a + β ( ϕ p ( D a + α u ( t ) ) ) = f ( t , u ( t ) ) , a < t < b , u j a = 0 , j = 0,1 , 2 , … , n - 2 , u ( α 1 ) ( b ) = ξ u ( α 1 ) ( η ) , ϕ p ( D a + α u ( a ) ) = 0 = D a + β 1 ( ϕ p ( D a + α u ( b ) ) ) , where β ∈ ( 1,2 ] , α ∈ ( n - 1 , n ] , n ≥ 3 , ξ ∈ ( 0 , ∞ ) , η ∈ ( a , b ) , β 1 ∈ ( 0,1 ] , α 1 ∈ { 1,2 , … , α - 2 } is a fixed integer, and ϕ p ( s ) = | s | p - 2 s , p > 1 , ϕ p - 1 = ϕ q , ( 1 / p ) + ( 1 / q ) = 1 , by applying Leggett–Williams fixed point theorems and fixed point index theory.