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.     

Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian

We consider the boundary value problems: (?p(x^′′(t)))+q(t)f(t,x(t),x(t−1),x^′(t))=0, ?p(s)=|s|^p−2s, p>1, t∈(0,1), subject to some boundary conditions. By using a generalization of the Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above problems.     

Eigenvalues and discrete boundary value problems for the one-dimensional p-laplacian

In this paper, we characterize the eigenvalues and show existence of positive solutions to discrete boundary value problem (here ?(s)=|s|^p−2s, p>1 and λ>0 is a parameter)

     

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 solutions.     

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.     

Multiple solutions to p-Laplacian problems with concave nonlinearities

In this paper we study the p-Laplacian type elliptic problems with concave nonlinearities. Using some asymptotic behavior of f at zero and infinity, three nontrivial solutions are established.     

Positive solutions for three-point one-dimensional p-Laplacian boundary value problems with advanced arguments

This paper considers the existence of positive solutions for advanced differential equations with one-dimensional p-Laplacian. To obtain the existence of at least three positive solutions we use a fixed point theorem due to Avery and Peterson.     

Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity

In this paper we deal with multiplicity of positive solutions to the p-Laplacian equation of the type

     

Positive solutions for higher order singular p-Laplacian boundary value problems

This paper investigates 2m-th (m ≥ 2) order singular p-Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval.     

p-Laplacian boundary value problems on exterior regions

This paper treats some variational principles for solutions of inhomogeneous p  -Laplacian boundary value problems on exterior regions U?R^N$U?{\mathbb{R}}^N$ with dimension N?3$N?3$. Existence-uniqueness results when p∈(1,N)$p\in (1,N)$ are provided in a space E^1,p(U)$E^{1,p}(U)$ of functions that contains W^1,p(U)$W^{1,p}(U)$. Functions in E^1,p(U)$E^{1,p}(U)$ are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an L^p$L^p$-imbedding theorem. Also an existence result for a general variational problem of this type is obtained.     

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.     

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.     

Superlinear discrete problems

The aim of this paper is to present an existence result of two positive solutions for a nonlinear difference problem by variational methods. The conclusion is achieved by assuming, together with the super-linearity at infinity, a suitable algebraic condition on the nonlinear term, which is more general than the sub-linearity at zero.     

Positive solutions for one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative

This paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one-dimensional p-Laplacian differential equation (?p^′(u^′))+a(t)f(u,u^′)=0, subject to some boundary conditions. We show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem.     

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

     

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.     

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

     

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.