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Multiple unbounded solutions for a boundary value problem on infinite intervals. (English) Zbl 1275.34043

Summary: This paper is concerned with the existence of multiple unbounded solutions for a Sturm-Liouville boundary value problem on the half-line. By assuming the existence of two pairs of unbounded upper and lower solutions, the existence of at least three solutions is obtained using degree theory. The Nagumo condition plays an important role in the nonlinear term involved in the first-order derivative. The method of unbounded upper and lower solutions is extended to obtain conditions for the existence of multiple solutions.

MSC:

34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B24 Sturm-Liouville theory
47N20 Applications of operator theory to differential and integral equations
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References:

[1] doi:10.1006/jmaa.2000.6887 · Zbl 1016.34010
[2] doi:10.1006/jdeq.2001.4056 · Zbl 1019.34015
[3] doi:10.1006/jdeq.2000.3797 · Zbl 1013.34017
[4] doi:10.1006/jmaa.2000.6798 · Zbl 0961.34004
[5] doi:10.1016/j.na.2007.08.005 · Zbl 1165.47044
[6] doi:10.1006/jmaa.1995.1367 · Zbl 0852.34019
[7] doi:10.1112/S0025579300016120 · Zbl 1049.34033
[8] doi:10.1016/j.na.2004.02.021 · Zbl 1053.34028
[9] doi:10.1016/j.cam.2005.11.010 · Zbl 1116.34016
[10] doi:10.1016/j.na.2008.03.049 · Zbl 1167.34320
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