Tobias Weth
On nodal solutions to generalized Emden-Fowler equations
(74K, LaTeX 2e)

ABSTRACT.  We introduce a new variational method in order to derive results concerning
existence and nodal properties of solutions to superlinear equations, and we
focus on applications to the equation   
\begin{eqnarray*}   
&-\Delta u = h(x,u)\\   
&u \in L^{\frac{2N}{N-2}}(\rz^N),\quad \nabla u \in L^2(\rz^N),\quad N\ge 3   
\end{eqnarray*}   
where $h$ is a Caratheodory function which is odd in $u$. In the particular case 
where $h$ is radially symmetric, we prove, for given $n \in \nz$, 
the existence of a solution having precisely $n$ nodal domains, whereas some 
results also pertain to a nonsymmetric nonlinearity.