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This paper discusses the existence of solutions of the fractional differential equations c D µ (φ(c D α u)) = F u, c D µ (φ(c D α u)) = f (t, u, c D ν u) satisfying the boundary conditions u(0) = A(u), u(T) = B(u). D is the Caputo fractional derivative, φ ∈ C(−a, a) (a > 0), F is a continuous operator, A, B are bounded and continuous functionals and f ∈… (More)

In this paper we study the existence and uniqueness of solutions to a nonlinear Neumann problem for a scalar second order ordinary differential equation u = a t u + f (t, u, u), where a < 0, and f (t, x, y) satisfies the local Carathéodory conditions on [0, T ] × R × R. 1 Motivation The aim of this work is to show the existence and uniqueness of solutions… (More)

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet boundary value problem (φ(u)) = λ[ f (t, u, u) + h(t, u, u)], u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and h may be singular at the value 0 of its… (More)

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