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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.

MSC:

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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