Existence Results for a Dirichlet Quasilinear Elliptic Problem


Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran


In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.


1. G. Bonanno, A critical point theorem via the Ekeland variational principle, Nonlinear Anal. 75 (2012), 2992-3007.
2. J.R. Graef, S. Heidarkhani, L. Kong, A critical points approach for the existence of multiple solutions of a Dirichlet quasilinear system, J. Math. Anal. Appl. 388 (2012), 1268-1278.
3. P. Pucci, J. Serrin, The strong maximum principle revisited, J. Differential Equations, 196 (2004) 1-66; Erratum, ibid., 207 (2004), 226-227.
4. B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401-410.