On log-weighted Adams' inequalities defined on ℝN and applications

In this paper, we establish some new functional inequalities of Adams’ type for radial Sobolev spaces of second order with logarithmic weights. The sharpness of these inequalities is also discussed. These inequalities (which can be singular) are new and complete the existing literature concerning this topic of research. Finally, we will end this work with a concrete application of these new inequalities to study some singular elliptic nonlinear equations involving new type of exponential growth condition at infinity.