Existence results for a nonlinear neutron transport equation with elastic and inelastic collision operators in L p -spaces

Abstract

In this paper, we discuss the existence of solutions to a stationary neutron transport equation involving elastic and inelastic collision operators in L p - espaces ( 1 ≤ p < ∞ ) . For 1 < p < ∞ , we use the Krasnosel'slii fixed point theorem and the compactness which involved by the averaging result for neutron transport equation. For p = 1, our approach is different, it uses the measure of weak noncompactness of De Blasi, the concepts of Dunford–Pettis operators together with a recent version of Krasnosel'skii's fixed point theorem involving ws-compact and ww-compact operators and the weak compactness.