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Existence and concentration of nodal solutions for a subcritical p&q equation

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Gustavo S. Costa and Giovany M. Figueiredo were partially supported by CNPq, Capes and Fapesp - Brazil
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  • In this paper we prove existence and concentration results for a family of nodal solutions for a some quasilinear equation with subcritical growth, whose prototype is

    $ -\Delta_{p}u- \Delta_{q}u+V( x)(|u|^{p-2}u+|u|^{q-2}u) = f(u) \quad \mbox{in} \ \mathbb{R}^{N}. $

    Each nodal solution changes sign exactly once in $ \mathbb{R}^{N} $ and has an exponential decay at infinity. Here we use variational methods and Del Pino and Felmer's technique [10] in order to overcome the lack of compactness.

    Mathematics Subject Classification: Primary: 35J60; Secondary: 35J10, 35J20.


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