Boundary value problems for second order nonlinear differential equations on infinite intervals

In this paper, we consider boundary value problems for nonlinear differential equations on the semi-axis <f>(0,∞)</f> and also on the whole axis <f>(−∞,∞)</f>, under the assumption that the left-hand side being a second order linear differential expression belongs to the Weyl limit-circle case. The boundary value problems are considered in the Hilbert spaces <f>L2(0,∞)</f> and <f>L2(−∞,∞)</f>, and include boundary conditions at infinity. The existence and uniqueness results for solutions of the considered boundary value problems are established. [Copyright &y& Elsevier]