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Infinitely many solutions of a symmetric Dirichlet problem. (English) Zbl 0799.35071
We seek solutions $u=(u\sb 1,\dots, u\sb m): \overline{\Omega} \to \bbfR\sp m$ of the nonlinear Dirichlet problem $$\Delta u+F\sb u(u)=u \quad \text{in }\Omega, \qquad u=0 \quad \text{on } \partial\Omega. \tag D$$ Here $\Omega$ is a bounded domain in $\bbfR\sp n$ with smooth boundary and $F: \bbfR\sp m \to\bbfR$ is $C\sp 1$ and satisfies certain growth conditions. We investigate which kind of symmetries guarantee the existence of infinitely many solutions of (D).

MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
58J70Invariance and symmetry properties
35J20Second order elliptic equations, variational methods
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References:
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