Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on Rⁿ

The existence/nonexistence question is studied for the inhomogeneous elliptic equation Δu + u^p + μf(x) = 0 in Rⁿ. In particular, we establish that the above equation possesses infinitely many positive entire solutions for small μ > 0 provided that n ≥ 11, p is large enough, and the locally Hölder continuous function f satisfies suitable decay conditions at ∞.