We study existence and multiplicity results for solutions of elliptic problems of the type −∆u = g(x, u) in a bounded domain Ω with Dirichlet boundary conditions. The function g(x, s) is asymptotically linear as |s| → +∞. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type −∆u = gε (x, u) where gε (x, s) → g(x, s) as ε → 0. The previous results find an application in the study of Dirichlet problems of the type −∆u = g(x, u) + μ where μ is a Radon measure. To properly set the above mentioned problems in a variational framework we also study existence and properties of critical points of a class of abstract nonsmooth functional defined on Banach spaces and extend to this nonsmooth framework some classical linking theorems.
Multiplicity results for a class of asymptotically linear elliptic problems with resonance and applications to problems with measure data
SACCON, CLAUDIO
2010-01-01
Abstract
We study existence and multiplicity results for solutions of elliptic problems of the type −∆u = g(x, u) in a bounded domain Ω with Dirichlet boundary conditions. The function g(x, s) is asymptotically linear as |s| → +∞. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type −∆u = gε (x, u) where gε (x, s) → g(x, s) as ε → 0. The previous results find an application in the study of Dirichlet problems of the type −∆u = g(x, u) + μ where μ is a Radon measure. To properly set the above mentioned problems in a variational framework we also study existence and properties of critical points of a class of abstract nonsmooth functional defined on Banach spaces and extend to this nonsmooth framework some classical linking theorems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
