ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS

doi:10.1007/s10473-020-0203-9

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (2): 341-354.doi: 10.1007/s10473-020-0203-9

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ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS

Xian XU¹, Baoxia QIN², Zhen WANG¹

1. Department of Mathematics, Jiangsu Normal University, Xuzhou 221116, China;
2. School of Mathematics, Qilu Normal University, Jinan 250013, China

Received:2017-10-15 Revised:2019-05-08 Online:2020-04-25 Published:2020-05-26
Supported by:
This paper is supported by the National Natural Science Foundation of China (11871250), Qing Lan Project. Key (large) projects of Shandong Institute of Finance in 2019 (2019SDJR31), and the teaching reform project of Qilu Normal University (jg201710).

Abstract

Abstract: In this article, by employing an oscillatory condition on the nonlinear term, a result is proved for the existence of connected component of solutions set of a nonlocal boundary value 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 of the nonlinear problem for all parameter values in that interval.

Key words: Global solution branches, Leray-Schauder degree, asymptotic oscillation property

CLC Number:

47H07

Xian XU, Baoxia QIN, Zhen WANG. ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS[J].Acta mathematica scientia,Series B, 2020, 40(2): 341-354.

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ASYMPTOTIC BEHAVIOR OF SOLUTION BRANCHES OF NONLOCAL BOUNDARY VALUE PROBLEMS

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