The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problem {-Delta(p)u = g(x, u) in Omega, u - 0 on partial derivative Omega, where 1 < p < +infinity, Delta(p)u = div(vertical bar Delta u vertical bar(p-2)Delta u), Omega is an open bounded domain of R-N (N >= 3) with smooth boundary partial derivative Omega and the nonlinearity g behaves as u(p-1) at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981-1012, 1983), but extended to Banach spaces, and two sequences of quasi-eigenvalues for the p-Laplacian operator as in Candela and Palmieri (Calc. Var. 34: 495-530, 2009), Li and Zhou (J. Lond. Math. Soc. 65: 123-138, 2002).
p-Laplacian problems with nonlinearities interacting with the spectrum / Bartolo, Rossella; Candela, A. M.; Salvatore, A.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 20:5(2013), pp. 1701-1721. [10.1007/s00030-013-0226-1]
p-Laplacian problems with nonlinearities interacting with the spectrum
Bartolo, Rossella;
2013-01-01
Abstract
The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problem {-Delta(p)u = g(x, u) in Omega, u - 0 on partial derivative Omega, where 1 < p < +infinity, Delta(p)u = div(vertical bar Delta u vertical bar(p-2)Delta u), Omega is an open bounded domain of R-N (N >= 3) with smooth boundary partial derivative Omega and the nonlinearity g behaves as u(p-1) at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981-1012, 1983), but extended to Banach spaces, and two sequences of quasi-eigenvalues for the p-Laplacian operator as in Candela and Palmieri (Calc. Var. 34: 495-530, 2009), Li and Zhou (J. Lond. Math. Soc. 65: 123-138, 2002).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
