Get started
Work

Regularizing Effect of the Natural Growth Term in Quasilinear Problems with Sign-Changing Nonlinearities

Year: 2026
Type: article
Abstract: We investigate the existence and nonexistence of solutions to the Dirichlet problem where $$\Omega \subset \mathbb {R}^N$$ Ω ⊂ R N is a smooth bounded domain, $$p\in (1,\infty )$$ p ∈ ( 1 , ∞ ) , $$\lambda >0$$ λ > 0 and $$g\in C(\mathbb {R})$$ g ∈ C ( R ) . Our main assumption is that $$f:\mathbb {R}\rightarrow \mathbb {R}$$ f : R → R is a continuous function such that $$f(s)>0$$ f ( s ) > 0 for all $$s\in (\alpha ,\beta )$$ s ∈ ( α , β ) , where $$0<\alpha <\beta $$ 0 < α < β are two zeros of f . If $$f(0)\ge 0$$ f ( 0 ) ≥ 0 , we show that an area condition involving f and g is both sufficient and necessary in order to have a pair $$(\lambda ,u)\in \mathbb {R}^+\times {C^1_0(\overline{\Omega })}$$ ( λ , u ) ∈ R + × C 0 1 ( Ω ¯ ) , with $$u\ge 0$$ u ≥ 0 and $$\Vert u\Vert _{C(\overline{\Omega })}\in (\alpha ,\beta ]$$
DOI: 10.1007/s00009-026-03107-1
Language: English
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4416692464
FWCI:
Cites:
Cited by:
Related to: