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October  2001, 7(4): 703-718. doi: 10.3934/dcds.2001.7.703

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

M. Grossi 1, , P. Magrone 2, and  M. Matzeu 2,

1. 

Dip. di Matematica, Università di Roma "La Sapienza", P.le A.Moro 2 - 00185 - Roma, Italy
2. 

Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma, Italy, Italy

Received  November 2000 Revised  March 2001 Published  July 2001

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, 35J2.
Citation: M. Grossi, P. Magrone, M. Matzeu. Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 703-718. doi: 10.3934/dcds.2001.7.703
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