Positive Solutions of Fourth-Order Equations under Nonlocal Boundary Value Conditions of Sturm-Liouville Type
Received:March 12, 2022  Revised:May 22, 2022
Key Words: positive solution   fixed point index   cone  
Fund Project:Supported by the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No.S202210145149).
Author NameAffiliation
Chunlei SONG Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China 
Wei CHEN Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China 
Guowei ZHANG Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China 
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Abstract:
      In this paper, we study the fourth-order problem with the first and second derivatives in nonlinearity under nonlocal boundary value conditions of Sturm-Liouville type involving Stieltjes integrals. Some inequality conditions on nonlinearity are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone. Some examples are provided to support the main results under mixed boundary conditions containing multi-point with sign-changing coefficients and integral with sign-changing kernel.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.01.010
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