Multiple positive solutions for singular higher-order semipositone fractional differential equations with p-Laplacian

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C3 0, 1 as well as C2 0, 1 positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t 0, t 1, and u 0. The dual results for the other integral b...

Positive Periodic Solution for Second-Order Singular Semipositone Differential Equations

and Applied Analysis 3

Semipositone higher-order differential equations

Krasnoselskii’s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone conjugate and (n, p) problems. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Existence, Positive solution, Semipositone, Conjugate and (n,p) problems.

Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

and Applied Analysis 3 Lemma 2.1 see 8, 9 . 1 If x ∈ L1 0, 1 , ρ > σ > 0, and n ∈ N, then IIx t I x t , DtIx t Iρ−σx t , 2.4 DtIx t x t , d dtn Dtx t Dt x t . 2.5 2 If ν > 0, σ > 0, then Dttσ−1 Γ σ Γ σ − ν t σ−ν−1. 2.6 Lemma 2.2 see 8 . Assume that x ∈ L1 0, 1 and μ > 0. Then IDtx t x t c1tμ−1 c2tμ−2 · · · cntμ−n, 2.7 where ci ∈ R i 1, 2, . . . , n , n is the smallest integer greater than or eq...