Advances in Differential Equations

Multiple solutions for a null mass Neumann problem in exterior domains

Marcelo F. Furtado, Liliane A. Maia, and Everaldo S. Medeiros

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In this paper we study the existence and multiplicity of solutions for the semilinear elliptic equation $-\Delta u = Q(x)f'(u)$ in an exterior domain with Neumann boundary conditions. We prove the existence of a positive ground state as well as a sign-changing solution under a double power growth condition on the nonlinearity.

Article information

Adv. Differential Equations, Volume 15, Number 1/2 (2010), 181-199.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations


Furtado, Marcelo F.; Maia, Liliane A.; Medeiros, Everaldo S. Multiple solutions for a null mass Neumann problem in exterior domains. Adv. Differential Equations 15 (2010), no. 1/2, 181--199.

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