Under a suitable condition on n and p, the quasilinear equation at critical growth -\Delta_p u=\lambda |u|^{p-2}u + |u|^{p^*-2} u is shown to admit a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda\geq\lambda_1. Nonstandard linking structures, for the associated functional, are recognized.
Degiovanni, M., Lancelotti, S., Linking solutions for p-Laplace equations with nonlinearity at critical growth, <<JOURNAL OF FUNCTIONAL ANALYSIS>>, 2009; 256 (11): 3643-3659. [doi:10.1016/j.jfa.2009.01.016] [http://hdl.handle.net/10807/3311]
Linking solutions for p-Laplace equations with nonlinearity at critical growth
Degiovanni, Marco;Lancelotti, Sergio
2009
Abstract
Under a suitable condition on n and p, the quasilinear equation at critical growth -\Delta_p u=\lambda |u|^{p-2}u + |u|^{p^*-2} u is shown to admit a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda\geq\lambda_1. Nonstandard linking structures, for the associated functional, are recognized.
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