Science and Technology Production
Article
Authorship
RAMOS QUOIRIN, HUMBERTO RODRIGO
;
Kenichiro Umezu
Date
2015
Publishing House and Editing Place
ACADEMIC PRESS INC ELSEVIER SCIENCE
Magazine
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ACADEMIC PRESS INC ELSEVIER SCIENCE
Summary
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We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. ...
We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work [19], where the case of sign-changing nonlinear boundary conditions is considered.
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Key Words
Semilinear elliptic problem;Bifurcation;Positive solution;Nonlinear boundary condition