This paper investigates the existence of positive solution for a boundary value problem of fractional differential equations with p-Laplacian operator. Our analysis relies on the research of properties of the corresponding Green's function. By the use of Krasnosel'skii's fixed-point theorem, the multiplicity results of some positive solutions are obtained.
In this paper, a fixed point theorem in a cone and some inequalities of the associated Green's function are applied to obtain the existence of positive solutions of second-order three-point boundary value problem with dependence on the first-order derivative x (t) + f (t, x(t), x (t)) = 0, 0 < t < 1, x(0) = 0, x(1) = μx(η), where f : [0, 1] × [0, ∞) × R → [0, ∞) is a continuous function, μ > 0, η ∈ (0, 1), μη < 1. The interesting point is that the nonlinear term is dependent on the convection term.
This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. Finally, two examples are given to illustrate the main results.
In this paper, we study the multiple solutions for some second-order p-Laplace differential equations with three-point boundary conditions and instantaneous and noninstantaneous impulses. By applying the variational method and critical point theory the multiple solutions are obtained in a Sobolev space. Compared with other local boundary value problems, the three-point boundary value problem is less studied by variational method due to its variational structure. Finally, two examples are given to illustrate the results of multiplicity.
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