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

In this paper, we discuss the existence of solutions to a stationary neutron transport equation involving elastic and inelastic collision operators in $ L^p $ L p - espaces $ (1\leq p \lt \infty) $ (1 ≤ p < ∞). For $ 1 \lt p \lt \infty $ 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. [ABSTRACT FROM AUTHOR]