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# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Large versus bounded solutions to sublinear elliptic problems

### Tom 67 / 2019

Bulletin Polish Acad. Sci. Math. 67 (2019), 69-82 MSC: Primary 31D05, 35J08, 35J61; Secondary 31C05. DOI: 10.4064/ba8180-12-2018 Opublikowany online: 15 March 2019

#### Streszczenie

Let $L$ be a second order elliptic operator with smooth coefficients defined on a domain $\varOmega \subset \mathbb {R}^d$ (possibly unbounded), $d\geq 3$. We study nonnegative continuous solutions $u$ to the equation $L u(x) - \varphi (x, u(x))=0$ on $\varOmega$, where $\varphi$ is in the Kato class with respect to the first variable and it grows sublinearly with respect to the second variable. Under fairly general assumptions we prove that if there is a bounded nonzero solution then there is no large solution.

#### Autorzy

• Ewa DamekInstitute of Mathematics
Wrocław University
Pl. Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail
• Zeineb GhardallouDepartment of Mathematical
Analysis and Applications
University Tunis El Manar, LR11ES11
2092 El Manar 1, Tunis, Tunisia
e-mail

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