Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line. (English) Zbl 1021.34021

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.


34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47H10 Fixed-point theorems
47N20 Applications of operator theory to differential and integral equations
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