An inverse problem related to a half-linear eigenvalue problem
1 Center for General Education, National Quemoy University, Kinmen, 892, Taiwan, ROC
2 Department of Mathematics and Information Education, National Taipei University of Education, Taipei, 106, Taiwan, ROC
Boundary Value Problems 2014, 2014:65 doi:10.1186/1687-2770-2014-65Published: 24 March 2014
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.