01-143 Tobias Weth

On nodal solutions to generalized Emden-Fowler equations (74K, LaTeX 2e) 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}{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.

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