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A critical equation with Hardy potential Esposito, Pierpaolo


We discuss existence issues for a Dirichlet problem in bounded domains with polynomial nonlinearities of critical growth in presence of an Hardy potential. Linear perturbations can produce positive solutions and we aim to construct sign-changing solutions, shaped as a tower of "bubbles" centered at 0 with alternating signs. The construction is optimal in the radial case as a very fine asymptotic analysis shows for radial towers of "bubbles", recovering and improving what is known in the non-singular case. Joint work with N. Ghoussoub, A. Pistoia and G. Vaira.

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