An Orlicz space approach to exponential elliptic problems in higher dimensions
Abstract
Abstract We consider semilinear elliptic problems of the form $$ -\Delta u + \lambda u = f(x,u), \quad u\in H^1_0(A), $$ - Δ u + λ u = f ( x , u ) , u ∈ H 0 1 ( A ) , where $$A\subset \mathbb {R}^N$$ A ⊂ R N , $$N\ge 3$$ N ≥ 3 , is either a bounded or unbounded annulus, and $$\lambda \ge 0$$ λ ≥ 0 . We study a broad class of nonlinearities f with superlinear growth at infinity, including exponential- and power-type ones. Under suitable assumptions, we establish the existence of a positive nonradial solution via techniques in the spirit of Szulkin’s nonsmooth critical point theory, applied within a convex cone in Orlicz spaces. Notably, the Trudinger-Moser inequality fails in the whole Sobolev space $$H^1_0(A)$$ H 0 1 ( A ) .
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 65
- Issue
- 3
- Publication date
- 17 February 2026
- Language
- EN