Energy harvesting is the process of generating electrical energy from environmental sources such as solar panels. In recent years, this term has been frequently applied in the context of small autonomous devices such as wireless sensor nodes. The classical scheduling theory is insufficient for this kind of systems and new scheduling problems arise in this context. Until now, the research on this area focused in trying to improve the efficiency of existing algorithms. Our approach is to complete these efforts by a feasibility theory allowing us to understand why classical optimal algorithms are not efficient anymore with energy constraints. In this paper, we try to establish a schedulability test for a fixed priority real-time scheduling problem with energy constraints. We first introduce the problem and describe the model. Then, to illustrate the difficulty of the problem, we focus on a preemptive fixed priority scheduling policy where all the executions are postponed as long as possible. This policy lets the harvester the maximal amount of time to refill the battery. We call this policy P F PALAP for As Late As Possible. We try to define sufficient and/or necessary schedulability conditions and discuss its potential optimality under some additional assumptions. Then, through simple counter examples, we show that intuitive assumptions are wrong for this scheduling problem, making it very interesting to study.