On a Liouville-type equation with sign-changing weight
نویسندگان
چکیده
In this paper we study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems −∆u = λ (a(x)e + f(x, u)), u ∈ H 0 (Ω) where Ω is a bounded domain in R2 and λ > 0 is a parameter. The coefficient a(x) is allowed to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the TrudingerMoser inequality and variational methods. Note that when f(x, u) = 0 the equation is of Liouville type.
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