On an Asymptotic Boundary Value Problem for Second Order Differential Equations

Abstract

Abstract. The existence of at least one solution to a nonlinear second order differential equation in R k 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.

Existence theorems of nonlinear asymptotic BVP for a homeomorphism

“…For instance, in [12] the authors established the existence of unbounded solutions. Results for problems where the nonlinearity may change sign one can find for example in [8,14]. In [13], the asymptotic boundary condition x (∞) = 0 is replaced by x ∈ H 2 (R + ).…”