We establish in this paper the existence of infinitely many regular weak solutions of the prescribed mean curvature problem \begin{equation*} -{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \mbox{\, in $\Omega$}, \qquad \mathcal{B} u=0 \mbox{\, on $\partial \Omega$}. \end{equation*} where $\Omega$ is a bounded domain in $\RR^N$ with a $C^1$ boundary $\partial \Omega$, $\BB$ is either the Dirichlet, or the Neumann, or the mixed boundary operator, the function $f(x,s)$ is odd with respect to $s\in \RR$ and has a potential $F(x,s)=\int_0^s f(x,t)\,dt$ which is desultorily subquadratic at $s=0$, locally with respect to $x\in \Omega$. Our findings improve and extend in various directions previous results established in the literature.

### Infinitely many regular weak solutions for odd symmetric prescribed mean curvature problems

#### Abstract

We establish in this paper the existence of infinitely many regular weak solutions of the prescribed mean curvature problem \begin{equation*} -{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \mbox{\, in $\Omega$}, \qquad \mathcal{B} u=0 \mbox{\, on $\partial \Omega$}. \end{equation*} where $\Omega$ is a bounded domain in $\RR^N$ with a $C^1$ boundary $\partial \Omega$, $\BB$ is either the Dirichlet, or the Neumann, or the mixed boundary operator, the function $f(x,s)$ is odd with respect to $s\in \RR$ and has a potential $F(x,s)=\int_0^s f(x,t)\,dt$ which is desultorily subquadratic at $s=0$, locally with respect to $x\in \Omega$. Our findings improve and extend in various directions previous results established in the literature.
##### Scheda breve Scheda completa
2022
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3034864
##### Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

• ND
• ND
• ND