We study an inverse problem on the half-linear Dirichlet eigenvalue problem , where with and r is a positive function defined on . Using eigenvalues and nodal data (the lengths of two consecutive zeros of solutions), we reconstruct and its derivatives. Our method is based on (Law and Yang in Inverse Probl. 14:299-312, 779-780, 1998; Shen and Tsai in Inverse Probl. 11:1113-1123, 1995), and our result extends the result in (Shen and Tsai in Inverse Probl. 11:1113-1123, 1995) for the linear case to the half-linear case.
MSC: 34A55, 34B24, 47A75.