Erratum: Inverse nodal problem for p-Laplacian energy-dependent Sturm-Liouville equation

摘要

Theorem 2.1 [1] The eigenvaluesλnof the Dirichlet problem (1.3), (1.4) are λ2/pn=nπp+1p(nπp)p?1∫10q(t)dt+2p(nπp)p?22∫10r(t)dt+O(1np2). (2.4) Theorem 2.2 [1] For the problem (1.3), (1.4), the nodal point expansion satisfies xnj+1(nπp)p∫xnj0q(x)Sppdx+O(1np2+2).=jn+jpnp+1(πp)p∫10q(t)dt+2jpnp2+1(πp)p2∫10r(t)dt+2(nπp)p2∫xnj0r(x)Sppdx Proof Let λ=λn; integrating (2.3) from 0 to xnj, we have j?πpλ2/pn=xnj?∫xnj02r(x)λnSppdx?∫xnj0q(x)λ2nSppdx. By using the estimates of eigenvalues as 1λ2/pn=1nπp+1p(nπp)p+1∫10q(t)dt+2p(nπp)p2+1∫10r(t)dt+O(1np2+2), we obtain the result.?□