Work

An Orlicz space approach to exponential elliptic problems in higher dimensions

Year: 2026

Type: article

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 ) .

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03267-8

Authors: Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris, Federica Sani

Institutions: University of Turin, Politecnico di Milano, University of Modena and Reggio Emilia

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Università degli Studi di Torino