Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line (Q1849017)

The objective of the paper is to prove the existence of unbounded solutions to the following boundary value problem \((1/p(t))(p(t)x'(t))'+f(t,x(t))=0,\) \(t>0.\) Sufficient conditions are stated. The author considers a special Banach space \(C_\infty.\) To prove the results, the author relies on the nonlinear alternative and a theorem of Corduneanu. The existence of multiple unbounded solutions is also discussed using fixed-point index theory. Two examples are given to illustrate the results.