On the Fučík spectrum of the scalar p-Laplacian with indefinite integrable weights
1 Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, People’s Republic of China
2 Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
Boundary Value Problems 2014, 2014:10 doi:10.1186/1687-2770-2014-10Published: 9 January 2014
In this paper, we study the structure of the Fučík spectrum of Dirichlet and Neumann problems for the scalar p-Laplacian with indefinite weights . Besides the trivial horizontal lines and vertical lines, it will be shown that, confined to each quadrant of , is made up of zero, an odd number of, or a double sequence of hyperbolic like curves. These hyperbolic like curves are continuous and strictly monotonic, and they have horizontal and vertical asymptotic lines. The number of the hyperbolic like curves is determined by the Dirichlet and Neumann half-eigenvalues of the p-Laplacian with weights a and b. The asymptotic lines will be estimated by using Sturm-Liouville eigenvalues of the p-Laplacian with a weight a or b.
MSC: 34B09, 34B15, 34L05.