Second order boundary value problems on an unbounded domain Original Research Article

We consider the second order nonlinear differential equation View the MathML source(p(t)u′(t))′=f(t,u(t),u′(t)),a.e. in (0,∞), Turn MathJax on satisfying two sets of boundary conditions: View the MathML sourceu′(0)=0,limt→∞u(t)=0 Turn MathJax on and View the MathML sourceu(0)=0,limt→∞u(t)=0, Turn MathJax on where f:[0,∞)×R2→Rf:[0,∞)×R2→R is Carathéodory with respect to L1[0,∞)L1[0,∞), p∈C[0,∞)∩C1(0,∞)p∈C[0,∞)∩C1(0,∞) and p(t)>0p(t)>0 for all t≥0t≥0. We obtain the existence of at least one solution using the Leray–Schauder Continuation Principle.