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| Much of the literature on entire solutions for semilinear elliptic equations with superlinear growth focuses on positive solutions (or "ground states"). Typically, positive entire solutions do not exist if the growth of the nonlinearity is subcritical in a certain sense. A natural question, then, is whether there are sign-changing entire solutions in such cases. We will present recent and ongoing work on the existence, uniqueness up to scaling and symmetry, and asymptotic behavior of oscillatory entire radial solutions for a subcritical biharmonic equation with power nonlinearity and discuss possible generalizations to the polyharmonic case. |
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