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

JUAN PABLO PINASCO; CRISTIAN SCAROLA

JOURNAL OF DIFFERENTIAL EQUATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016 vol. 261 p. 1000 - 1016

0022-0396

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.