Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory

and Applied Analysis 3 A3 lim inf|x|→ ∞ ∇F t, x , x − 2F t, x /|x|μ ≥ Q > 0 uniformly for some Q > 0 and a.e. t ∈ 0, T , where r > 2 and μ > r − 2. We state our first existence result as follows. Theorem 1.1. Assume that (A1)–(A3) hold and that F t, x satisfies the condition (A). Then BVP 1.1 has at least one solution on E. 1.2. The Asymptotically Quadratic Case For the asymptotically quadratic...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

and Applied Analysis 3 ii If γ n − 1 and f ∈ ACn−1 a, b ,R , then CaD t f t and t Dn−1 b f t are represented by C aD n−1 t f t f n−1 t , t D n−1 b f t −1 n−1 f n−1 t , t ∈ a, b . 2.3 With these definitions, we have the rule for fractional integration by parts, and the composition of the Riemann-Liouville fractional integration operator with the Caputo fractional differentiation operator, which ...

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Solvability of an impulsive boundary value problem on the half-line via critical point theory

In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.