Existence of positive entire solutions of semilinear elliptic equations Original Research Article

For n≥3n≥3 and p>1p>1, the elliptic equation Δu+K(x)up+f(x)=0Δu+K(x)up+f(x)=0 in View the MathML sourceRn possesses a positive entire solution under proper conditions on locally Hölder continuous functions KK and ff. After obtaining a priori estimates on decay of solutions near ∞∞, we study the existence of positive solutions, and present necessary conditions of ff for the existence.