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Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications
Author
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-01-09
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞)) is a radially symmetric weighted function and m(r):=m(x)≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+), but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞).
Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.
American Psychological Association (APA)
Shen, Wenguo. 2018. Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1186712
Modern Language Association (MLA)
Shen, Wenguo. Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications. Journal of Function Spaces No. 2018 (2018), pp.1-7.
https://search.emarefa.net/detail/BIM-1186712
American Medical Association (AMA)
Shen, Wenguo. Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-7.
https://search.emarefa.net/detail/BIM-1186712
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186712