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Symmetry Results For Solutions of a Semilinear Nonhomogeneous Problem

Abstract In this paper we show the axial symmetry of a particular type of solutions of the following semilinear nonhomogeneous problem where B is the unit ball of ℝN, N ≥ 3, u+ = 0 if u < 0 and φ1(x) > 0 is the eigenfunction of -Δ corresponding to the first eigenvalue λ1, with Dirichlet boundary conditions. The solutions considered exhibit one or two peaks and concentrate, as the parameter s goes to +∞.