Scalar multi-point boundary value problems at resonance

First-order three-point boundary value problems at resonance

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Solvability of functional differential equations with multi-point boundary value problems at resonance

In this paper, we discuss the following third order functional differential equations x (t) = f (t, x(t), (Fx)(t), x (t), (Gx )(t), x (t), (Hx )(t)), t ∈ [0, 1], subject to the boundary conditions x(0) = 0, x (0) = 0, x (1) = m−2 ∑ i=1 αi x (ηi ), where f : [0, 1] × R6 −→ R, F,G, H are three operators, αi (i = 1, . . . ,m − 2) ≥ 0, 0 < η1 < η2 < · · · < ηm−2 < 1. Under some appropriate conditio...

Positive Solutions for Second-order Multi-point Boundary-value Problems at Resonance in Banach Spaces

In this article, we study the existence and multiplicity of positive solutions for a nonlinear second-order multi-point boundary-value problem at resonance in Banach spaces. The arguments are based upon a specially constructed equivalent equation and the fixed point theory in a cone for strict set contraction operators.

Multi-point Boundary-value Problems for the P-laplacian at Resonance

In this paper, we consider multi-point boundary-value problems for the p-laplacian at resonance. Applying an extension of Mawhin’s continuation theorem, we show the existence of at least one solution.