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Semilinear elliptic problems near resonance with a nonprincipal eigenvalue. (English) Zbl 1149.35044
Summary: We consider the Dirichlet problem for the equation -Δu=λu±f(x,u)+h(x) in a bounded domain, where f has a sublinear growth and hL 2 . We find suitable conditions on f and h in order to have at least two solutions for λ near to an eigenvalue of -Δ. A typical example to which our results apply is when f(x,u) behaves at infinity like a(x)|u| q-2 u, with M>a(x)>δ>0, and 1<q<2.
MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35P05General topics in linear spectral theory of PDE
58J50Spectral problems; spectral geometry; scattering theory
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