A nodal inverse problem for a quasi-linear ordinary differential equation in the half-line

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Pinasco, Juan P.¹  Scarola, Cristian² 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, IMAS CONICET, Dept Matemat, Ciudad Univ,Pab 1,Int Guiraldes 2160, RA-1428 Buenos Aires, DF, Argentina

[2] Univ Nacl La Pampa, Fac Ciencias Exactas & Nat, Uruguay 151, RA-6300 Santa Rosa, La Pampa, Argentina

关键词: Inverse problems;    Eigenvalues;    Nodal points;    Singular problem;    p-Laplacian;   

DOI  :  10.1016/j.jde.2016.03.031

来源: Elsevier

【 摘 要 】

In this paper we study an inverse problem for a quasi-linear ordinary differential equation with a monotonic weight in the half-line. First, we find the asymptotic behavior of the singular eigenvalues, and we obtain a Weyl-type asymptotics imposing an appropriate integrability condition on the weight. Then, we investigate the inverse problem of recovering the coefficients from nodal data. We show that any dense subset of nodes of the eigenfunctions is enough to recover the weight. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free