Multiple Positive Solutions for Singular Quasilinear Multipoint BVPs with the First-Order Derivative

Multiple Positive Solutions for Singular Quasilinear Multipoint BVPs with the First-Order Derivative

The existence of at least three positive solutions for differential equation φp u′ t ′ g t f t, u t , u′ t 0, under one of the following boundary conditions: u 0 ∑m−2 i 1 aiu ξi , φp u ′ 1 ∑m−2 i 1 biφp u ′ ξi or φp u′ 0 ∑m−2 i 1 aiφp u ′ ξi , u 1 ∑m−2 i 1 biu ξi is obtained by using the H. Amann fixed point theorem, where φp s |s|p−2s, p > 1, 0 < ξ1 < ξ2 < · · · < ξm−2 < 1, ai > 0, bi > 0, 0 <...

Existence and multiplicity of positive solutions for singular quasilinear problems

In this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p-Laplacian problems. In the first two theorems we prove the existence of solutions in the sense of distributions. By strengthening the hypotheses, in the third and last result, we establish the existence of two ordered positive weak soluti...

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

Multiplicity of Positive Solutions for a Fourth-Order Quasilinear Singular Differential Equation

This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation (|u|u) = λg(t)f(u), 0 < t < 1, where p > 1, λ > 0. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold λ < +∞, such that if 0 < λ ≤...

Positive Periodic Solutions of Singular First Order Functional Difference Equation

In this paper, we consider the following singular first order functional difference equation Δx(k) = −a(k)x(k) + λb(k)f(x(k − τ(k))), k ∈ Z where f(.) is singular at x = 0. By using a Kranoselskii fixed point theorem, we will establish the existence and multiplicity of positive periodic solutions for the above problem. The results obtained are new, and some examples are given to illustrate our ...