A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities

We study the bifurcation diagrams of positive solutions of the two point boundary value problem

     

A complete classification of bifurcation diagrams of classes of a multiparameter Dirichlet problem with concave-convex nonlinearities

We study the bifurcation diagrams of positive solutions of the multiparameter Dirichlet problem

     

Classification of bifurcation diagrams of a p-Laplacian Dirichlet problem with examples

We study bifurcation diagrams of positive solutions of the p-Laplacian Dirichlet problem

     

A complete classification of bifurcation diagrams of a p-Laplacian Dirichlet problem

We study the bifurcation diagrams of classical positive solutions u with ‖u_‖∞∈(0,∞) of the p-Laplacian Dirichlet problem

     

The structure of the solution set of a generalized Ambrosetti-Brezis-Cerami problem in one space variable

We study the structure of solution set of the nonlinear two-point boundary value problem

     

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

     

Bifurcation diagrams of a p-Laplacian Dirichlet problem with Allee effect and an application to a diffusive logistic equation with predation

We study bifurcation diagrams of positive solutions for the p-Laplacian Dirichlet problem

     

Exact multiplicity results for a class of two-point boundary value problems

This paper is concerned with the exact number of positive solutions for boundary value problems ^′(|y^′|^p−2y^′)+λf(y)=0 and y(−1)=y(1)=0, where p>1 and λ>0 is a positive parameter. We consider the case in which the nonlinearity f is positive on (0,∞) and (p−1)f(u)−uf^′(u) changes sign from negative to positive.     

Positive solutions of a second-order integral boundary value problem

In this paper we study the existence of positive solutions of a second-order integral boundary value problems for ordinary differential equations. Our results presented here unify, generalize and substantially improve the existing results in the literature. Moreover, it is worthwhile to point out that our method will dispense with constructing a new Green function.     

Three positive solutions of a nonlinear three-point boundary value problem

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem

     

Positive solutions for a three-point boundary value problem at resonance

This paper deals with the second order three-point boundary value problem

     

Positive solutions of a general discrete boundary value problem

In this paper, the existence of positive solutions for a nonlinear general discrete boundary value problem is established. Such results extend and improve some known facts for the two-point and three-point boundary value problems. Particularly, the boundary value conditions can be nonlinear and the method is new. For explaining the main results, some numerical examples are also given.     

Positive solutions for nonlinear three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T. Consider the following three-point boundary value problem on time scales:

     

Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T, β,γ?0 and 0<η<ρ(T). We consider the following p-Laplacian three-point boundary problem on time scales

     

Exact multiplicity and ordering properties of positive solutions of a p-Laplacian Dirichlet problem and their applications

We study the exact multiplicity and ordering properties of positive solutions of the p-Laplacian Dirichlet problem

     

On the existence of positive solutions for a class of singular boundary value problems

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C¹[0,1]∩C²(0,1) or C[0,1]∩C²(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.     

Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

The set of steady state solutions to a reaction-diffusion equation modeling an autocatalytic chemical reaction is completely determined, when the reactor has spherical geometry, and the spatial dimension is n=1 or 2 for any reaction order, or n?3 for subcritical reaction order. Bifurcation approach and analysis of linearized problems are used to establish exact multiplicity and precise global bifurcation diagram of positive steady states.