Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 269, pp. 1-15.
Solution branches for nonlinear problems with an
asymptotic oscillation property
Lin Gong, Xiang Li, Baoxia Qin, Xian Xu
Abstract:
In this article we employ an oscillatory condition on the nonlinear term,
to prove the existence of a connected component of solutions
of a nonlinear problem, which bifurcates from infinity and asymptotically
oscillates over an interval of parameter values.
An interesting and immediate consequence of such oscillation property of
the connected component is the existence of infinitely many solutions
to the nonlinear problem for all parameter values in that interval.
Submitted August 20, 2015. Published October 19, 2015.
Math Subject Classifications: 47H07, 47H10.
Key Words: Global solution branch; fixed point index;
asymptotic oscillation property.
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Lin Gong
Department of Mathematics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: gonglin812@163.com
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Xiang Li
Department of Mathematics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: lxws3@126.com
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Baoxia Qin
School of Mathematics
Qilu Normal University
Jinan, Shandong 250013, China
email: qinbaoxia@126.com
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Xian Xu
Department of Mathematics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: xuxian68@163.com
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