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

  • Ziyatkhan S. Aliyev

    Baku State University and Institute of Mathematics and Mechanics, NAS of Azerbaijan, Baku, Azerbaijan
  • Shanay M. Hasanova

    Institute of Mathematics and Mechanics, NAS of Azerbaijan, Baku, Azerbaijan
Global Bifurcation of Positive Solutions of Semi-Linear Elliptic Partial Differential Equations with Indefinite Weight cover
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Abstract

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.

Cite this article

Ziyatkhan S. Aliyev, Shanay M. Hasanova, Global Bifurcation of Positive Solutions of Semi-Linear Elliptic Partial Differential Equations with Indefinite Weight. Z. Anal. Anwend. 38 (2019), no. 1, pp. 1–15

DOI 10.4171/ZAA/1625