J Elliptic Parabol Equ https://doi.org/10.1007/s41808-018-0019-0 Existence of positive entire solutions of fully nonlinear elliptic equations Antonio Vitolo Received: 15 September 2017 / Accepted: 4 May 2018 © Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper we try to generalize a well known result due to Brezis on the existence of weak solutions in the whole space to second-order fully nonlinear equations with an absorption term satisfying a Keller–Osserman condition plus an additive external source without growth condition at infinity. We also discuss con - stant sign solutions. Keywords Entire solutions · Existence and uniqueness · Fully nonlinear elliptic equations Mathematics Subject Classification 35J60 · 35J61 · 35J25 · 35D40 1 Introduction This paper is inspired by the pioneeristic result by Brezis  who was able to show exist- ence and uniqueness of entire solutions in distributional sense for the semilinear equation p−1 Δu = u u + h(x) (1) 1 n with p > 1 , assuming h ∈ L (ℝ ). loc The above result was generalized to viscosity solutions of fully nonlinear second- order uniformly elliptic equations 2 p−1 H(D u)= u u + h(x) (2) n n by Esteban et al. , assuming h ∈ L (ℝ
Journal of Elliptic and Parabolic Equations – Springer Journals
Published: May 29, 2018
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