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arXiv · 1406.5448

Entire solutions for a class of fourth order semilinear elliptic equations with weights

Paolo Caldiroli·Gabriele Cora
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Abstract

We investigate the problem of entire solutions for a class of fourth order, dilation invariant, semilinear elliptic equations with power-type weights and with subcritical or critical growth in the nonlinear term. These equations define non compact variational problems and are characterized by the presence of a term containing lower order derivatives, whose strength is ruled by a parameter λ. We can prove existence of entire solutions found as extremal functions for some Rellich-Sobolev type inequalities. Moreover, when the nonlinearity is suitably close to the critical one and the parameter λ is large, symmetry breaking phenomena occur and in some cases the asymptotic behavior of radial and non radial ground states can be somehow described.

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Paolo Caldiroli, Gabriele Cora. 2014-06-20. Entire solutions for a class of fourth order semilinear elliptic equations with weights. https://arxiv.org/abs/1406.5448

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