Existence and Multiplicity of Solutions to Elliptic Problems with Discontinuities and Free Boundary Conditions
نویسندگان
چکیده
We study the nonlinear elliptic problem with discontinuous nonlinearity −∆u = f(u)H(u− μ) in Ω, u = h on ∂Ω, where H is the Heaviside unit function, f, h are given functions and μ is a positive real parameter. The domain Ω is the unit ball in Rn with n ≥ 3. We show the existence of a positive solution u and a hypersurface separating the region where −∆u = 0 from the region where −∆u = f(u). Our method relies on the implicit function theorem and bifurcation analysis.
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