Computing eigenvalues and Fučik-spectrum of the radially symmetric p-Laplacian

摘要

Eigenvalue problems for the radially symmetric p-Laplacian are discussed. We present algorithms which compute a given number of eigenvalues and Fučik-curves together with the corresponding eigenfunctions. The second-order p-Laplacian equation is transformed into a first-order system by a generalized Prüfer-transformation. To the first-order system we apply shooting algorithms, Newton's method and in case of the Fučik-curves a predictor–corrector method. Our approach requires analytical and numerical treatment of generalized sine-functions. Singular as well as regular problems are treated, and a detailed error analysis for the approximation of singular problems by regular ones are given. Numerical results are presented.