Positive solutions for non-homogeneous semilinear elliptic equations with data that changes sign

Source abstract

Let Ω ⊂ R N be a bounded domain. We consider the nonlinear problem and prove that the existence of positive solutions of the above nonlinear problem is closely related to the existence of non-negative solutions of the following linear problem: . In particular, if p > ( N + 2)/( N − 2), then the existence of positive solutions of nonlinear problem is equivalent to the existence of non-negative solutions of the linear problem (for more details, we refer to theorems 1.2 and 1.3 in § 1 of this paper).