Semilinear elliptic problems near resonance with a nonprincipal eigenvalue |
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| Authors: | Francisco Odair de Paiva Eugenio Massa |
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| Institution: | a IMECC-UNICAMP, C.P. 6065, 13081-970 Campinas-SP, Brazil
b Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos-SP, Brazil |
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| Abstract: | 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 h∈L2. 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−2u, with M>a(x)>δ>0, and 1<q<2. |
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| Keywords: | Semilinear elliptic equations Multiplicity of solutions Quasi resonant problems Saddle point geometry |
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