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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth

Pages: 703 - 718, Volume 7, Issue 4, October 2001

doi:10.3934/dcds.2001.7.703       Abstract        Full Text (208.5K)       Related Articles

M. Grossi - Dip. di Matematica, Università di Roma "La Sapienza", P.le A.Moro 2 - 00185 - Roma, Italy (email)
P. Magrone - Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma, Italy (email)
M. Matzeu - Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma, Italy (email)

Abstract: In this paper we state some existence results for the semilinear elliptic equation $-\Delta u(x)-\lambda u(x) = W(x)f(u)$ where $W(x)$ is a function possibly changing sign, $f$ has a superlinear growth and $\lambda$ is a positive real parameter. We discuss both the cases of subcritical and critical growth for $f$, and prove the existence of Linking type solutions.

Keywords:  Critical exponent, linking type critical points, potential changing sign.
Mathematics Subject Classification:  35J65, 35J20, 35J25.

Received: November 2000;      Revised: March 2001;      Published: July 2001.