Fractional equations with indefinite nonlinearities

In this paper, we consider a fractional equation with indefinite nonlinearities {document}(- )α/2 u = a(x₁) f(u) {document} for $0<α<2$, where a and f are nondecreasing functions. We prove that there is no positive bounded solution. In particular, in the case a(x₁) = x₁ and f(u) = uᵖ, this remarkably improves the result in [15] by extending the range of $α$ from $[1,2)$ to $(0,2)$, due to the introduction of new ideas, which may be applied to solve many other similar problems.