Electron. J. Diff. Equ., Vol. 2015 (2015), No. 119, pp. 1-16.

Existence of infinitely many sign-changing solutions for elliptic problems with critical exponential growth

Denilson S. Pereira

Abstract:
In this work we prove the existence of infinitely many nonradial solutions, that change sign, to the problem
$$\displaylines{ -\Delta u=f(u)\quad\text{in }B\cr u=0\quad\text{on }\partial B, }$$
where B is the unit ball in $\mathbb{R}^2$ and f is a continuous and odd function with critical exponential growth.

Submitted January 29, 2015. Published April 30, 2015.
Math Subject Classifications: 35A15, 35J15.
Key Words: Variational method; critical exponential growth; sign-changing solution.

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Denilson S. Pereira
Universidade Federal de Campina Grande
Unidade Acadêmica de Matemética - UAMat
CEP: 58.429-900 - Campina Grande - PB, Brazil
email: denilsonsp@dme.ufcg.edu.br

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