PageHeader : Punkcialaj $\mathrm{E}\mathrm{k}\mathrm{v}\mathrm{a}\mathrm{c}\dot{\mathrm{l}\mathrm{t}}\mathrm{o}\mathrm{j}$ , 9 (1966), 1-7 Title : A New Construction of Barrier Functions AuthorInfo : By Kiyoshi AKO AuthorInfo : (University of Tokyo) section : Introduction section : 1. Assumptions on the equation (1). section : 2. Regular boundary points. section : 3. Main result. section : 4. Proof of Theorem 1. section : 5. Proof of Theorem 1 (continued). section : 6. A remark on Theorem 1. section : 7. Quasilinear case. section : 8. Linear case.