Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on ${\bf R}^n$

Abstract.

The existence/nonexistence question is studied for the inhomogeneous elliptic equation $\Delta u + u^p +\mu f(x)=0$ in ${\bf R}^n$. In particular, we establish that the above equation possesses infinitely many positive entire solutions for small $\mu>0$ provided that $n\geq11$, p is large enough, and the locally Hölder continuous function f satisfies suitable decay conditions at $\infty$.