Existence of solutions of anisotropic elliptic equations with nonpolynomial nonlinearities in unbounded domains
Larisa Mikhailovna Kozhevnikova, Anna Alexandrovna Khadzhi · Sbornik Mathematics · 2015
The paper is concerned with the solvability of the Dirichlet problem for a certain class of anisotropic elliptic second-order equations in divergence form with low-order terms and nonpolynomial nonlinearities The Caratheodory functions , , are assumed to satisfy a joint monotonicity condition in the arguments , . Constraints on their growth in are formulated in terms of a special class of convex functions. The solvability of the Dirichlet problem in unbounded domains , , is investigated. An existence theorem is proved without making any assumptions on the behaviour of the solutions and their growth as . Bibliography: 26 titles.