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

M. Grossi; P. Magrone; M. Matzeu

doi:10.3934/dcds.2001.7.703

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2001, Volume 7, Issue 4: 703-718. Doi: 10.3934/dcds.2001.7.703

This issue Previous Article Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation Next Article Attractors for semilinear strongly damped wave equations on $\mathbb R^3$

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

1.
Dip. di Matematica, Università di Roma "La Sapienza", P.le A.Moro 2 - 00185 - Roma
2.
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma

Received: October 31, 2000

Revised: February 28, 2001

Published: September 2001

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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.

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Mathematics Subject Classification: 35J65, 35J20, 35J25.

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