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On second order nonlocal boundary value problem at resonance

Szymańska-Dębowska K.

Fasciculi Mathematici

2016

Nr 56

143--153

This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem x''=f(t,x), x' (0)=0, x' (1)-∫1 0 x(s)dg(s), where f ∶ [0,1] × Rk → Rk is continuous and g ∶ [0,1] → Rk is a function of bounded variation.

On an asymptotic boundary value problem for second order differential equations

Szymańska K.

Journal of Applied Analysis

2006

Vol. 12, nr 1

109-118

The existence of at least one solution to a nonlinear second order differential equation in Rκ on the semi-infinite with the first derivative vanishing at infinity is proved by using topological methods. The second boundary condition is x(0)=0 or x'(0)=0.