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Supercritical Elliptic Problems on Nonradial Domains via a Nonsmooth Variational Approach by Craig Cowan; Abbas Moameni is a Mathematics article available to read on EtoBox.
What is Supercritical Elliptic Problems on Nonradial Domains via a Nonsmooth Variational Approach about?
In this paper we are interested in positive classical solutions ofwhere is a bounded annular domain (not necessarily an annulus) in R N (N ≥ 3) and a(x) is a nonnegative continuous function. We show the existence of a classical positive solution for a range of supercritical values of p when the problem enjoys certain mild symmetry and monotonicity conditions. As a consequence of our results, we shall show that (1) has N 2 (the floor of N 2 ) positive nonradial solutions when a(x) = 1 and is an annulus with certain assumptions on the radii. We also obtain the existence of positive solutions in the case of toroidal domains. Our approach is based on a new variational principle that allows one to deal with supercritical problems variationally by limiting the corresponding functional on a proper convex subset instead of the whole space at the expense of a mild invariance property.
Who reads Supercritical Elliptic Problems on Nonradial Domains via a Nonsmooth Variational Approach?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Craig Cowan; Abbas Moameni
- Publisher
- Elsevier BV
- Published
- 2022
- Language
- EN
- Field
- Mathematics (Physical Sciences)