Existence and nonexistence of least energy nodal solution for a class of elliptic problem in R2

Claudianor Oliveira Alves, Denilson Pereira

DOI: http://dx.doi.org/10.12775/TMNA.2015.078

Abstract


In this work, we prove the existence of least energy nodal solutions for a class of elliptic problem in both cases, bounded and unbounded domain, when the nonlinearity has exponential critical growth in $\mathbb{R}^2$. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole $\mathbb{R}^{2}$.

Keywords


Variational methods; exponential critical growth; nodal solution

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