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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 1, 2019, pp. 1–15
DOI: 10.4171/ZAA/1625

Published online: 2019-01-07

Global Bifurcation of Positive Solutions of Semi-Linear Elliptic Partial Differential Equations with Indefinite Weight

Ziyatkhan S. Aliyev and Shanay M. Hasanova

In this paper we consider global bifurcation of solutions of nonlinear eigenvalue problems for second order uniformly elliptic equations with an indefinite weight function and the Dirichlet boundary condition. We show the existence of an unbounded continua contained in the classes of positive and negative functions and bifurcating from the points of the line of trivial solutions corresponding to the principal eigenvalues of the linearized problem.

Keywords: Uniformly elliptic equations, nonlinear eigenvalue problem, indefinite weight function, principal eigenvalue, global bifurcation

Aliyev Ziyatkhan, Hasanova Shanay: Global Bifurcation of Positive Solutions of Semi-Linear Elliptic Partial Differential Equations with Indefinite Weight. Z. Anal. Anwend. 38 (2019), 1-15. doi: 10.4171/ZAA/1625