Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian

In this paper, exact number of solutions are obtained for the one-dimensional p-Laplacian in a class of two-point boundary value problems. The interesting point is that the nonlinearity f is general form: f(u)=λg(u)+h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method.     

Triple positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales

A new triple fixed-point theorem is applied to investigate the existence of at least three positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales.     

Existence of three positive solutions for boundary value problems with p-Laplacian

By using fixed point theorem, we study the following equation g(u^′′(t))+a(t)f(u)=0 subject to boundary conditions, where g(v)=|v|^p−2v with p>1; the existence of at least three positive solutions is proved.     

Exact multiplicity of solutions and S-shaped bifurcation curves for the p-Laplacian perturbed Gelfand problem in one space variable

We study exact multiplicity of positive solutions and the bifurcation curve of the p-Laplacian perturbed Gelfand problem from combustion theory

     

On a class of singular p-Laplacian boundary value problems

We prove the existence and nonexistence of positive solutions for the boundary value problem

     

Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

Uniqueness results for the one-dimensional p-Laplacian

This paper is concerned with positive solutions of the boundary value problem ^′(|y^′|^p−2y^′)+f(y)=0, y(−b)=0=y(b) where p>1, b is a positive parameter. Assume that f is continuous on (0,+∞), changes sign from nonpositive to positive, and f(y)/yp−1 is nondecreasing in the interval of f>0. The uniqueness results are proved using a time-mapping analysis.     

Exact number of positive solutions for a class of semipositone problems

This paper is concerned with the boundary value problems y″+λ(y^p−y^q)=0 and y(−1)=y(1)=0, where p>q>−1 and λ>0 is a positive parameter. We discuss the existence of positive solutions and give a complete study.     

Existence of multiple positive solutions for nonlinear m-point boundary value problems

In this paper, we afford some sufficient conditions to guarantee   the existence of multiple positive solutions for the nonlinear m-point boundary value problem for the one-dimensional p-Laplacian

     

Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation (?p^′(u^′))+q(t)f(t,u,u^′)=0, t∈(0,1), subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems.     

Existence and iteration of positive solutions for a generalized right-focal boundary value problem with p-Laplacian operator

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following third-order generalized right-focal boundary value problem with p-Laplacian operator:

     

Multiple positive solutions to a three-point boundary value problem with p-Laplacian

Sufficient conditions are obtained that guarantee the existence of at least two positive solutions for the equation (g(u′(t)))′+a(t)f(u)=0 subject to boundary conditions, by a simple application of a new fixed-point theorem due to Avery and Henderson.     

Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator

In this paper, we consider the existence of positive solutions for the singular fourth-order p-Laplacian equation

     

Existence of triple positive solutions to a class of p-Laplacian boundary value problems

By using Leggett-Williams' fixed-point theorem, a class of p-Laplacian boundary value problem is studied. Sufficient conditions for the existence of triple positive solutions are established.     

The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator

In this paper, we study the existence of countable many positive solutions for a class of nonlinear singular boundary value systems with p-Laplacian operator:

     

Positive solutions of multi-point boundary value problems at resonance

We establish new results on the existence of positive solutions for some multi-point boundary value problems at resonance. Our results are based on a recent Leggett–Williams norm-type theorem due to O’Regan and Zima. We also derive a new result for a three-point problem, previously studied by several authors.     

Solution curves and exact multiplicity results for 2mth order boundary value problems

For any integer m?2, we consider the 2mth order boundary value problem

(−1)mu(2m)(x)=λg(u(x))u(x),x∈(−1,1),     

Solutions of two-point boundary value problems for even-order differential equations

The existence of solutions of the two-point boundary value problems consisting of the even-order differential equations

     

Multiple positive solutions for some p-Laplacian boundary value problems

This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian subject to one of the following boundary conditions: or where φ_p(s)=|s|^p−2s, p>1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.