MULTIPLE POSITIVE SOLUTIONS FOR SUPERLINEAR ELLIPTIC PROBLEM IN IR2 WITH SUBLINEAR NEUMANN BOUNDARY CONDITION

Let Ω ⊂ IR2 be a bounded domain with C 2 boundary. Let u ∈ H 1 (Ω) be a weak solution of the following problem: { −∆u + u = p(u)eu } (Pλ ) { u > 0 } ∂u in Ω, { ∂ν = λψuq on ∂Ω, } where α ∈ (0, 2], λ > 0, q ∈ [0, 1) and ψ a H lder continuous function on Ω.o α Here p(u) is a polynomial perturbation of eu as u → ∞. Using variational methods we show that there exists 0 Λ and atleast one solution when λ = Λ.