An inverse problem related to a half-linear eigenvalue problem

作者：Wang Wei Chuan^*; Cheng Yan Hsiou

来源：Boundary Value Problems, 2014, 2014(1): 65.

DOI：10.1186/1687-2770-2014-65

We study an inverse problem on the half-linear Dirichlet eigenvalue problem -(vertical bar y'(x)vertical bar(p-2)y'(x))' = (p-1)lambda r(x)vertical bar y(x)vertical bar(p-2)y(x), where p > 1 with p not equal 2 and r is a positive function defined on [0, 1]. Using eigenvalues and nodal data (the lengths of two consecutive zeros of solutions), we reconstruct r(-1/p)(x) 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.

• 出版日期2014-3-24