Energy dependent potential problems for the one dimensional p-Laplacian operator

CRISTIAN SCAROLA; JUAN PABLO PINASCO; HIKMET KOYUNBAKAN

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2019 vol. 45 p. 285 - 298

1468-1218

In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operatorwith zero Dirichlet boundary conditions. We assume that the problem has apotential which depends on the eigenvalue parameter, and we show that, for n bigenough, there exists a real eigenvalue λ n , and their corresponding eigenfunctionshave exactly n nodal domains.We characterize the asymptotic behavior of these eigenvalues, obtaining twoterms in the asymptotic expansion of λ n in powers of n.Finally, we study the inverse nodal problem in the case of energy dependentpotentials, showing that some subset of the zeros of the corresponding eigenfunctionsis enough to determine the main term of the potential.