 01143 Tobias Weth
 On nodal solutions to generalized EmdenFowler equations
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Apr 11, 01

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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}{N2}}(\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.
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