Differential and Integral Equations

On the exterior Neumann problem with critical growth

J. Chabrowski

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In this paper we investigate the solvability of the nonlinear Neumann problem (1.1) involving a critical Sobolev nonlinearity in an exterior domain. We examine the common effect of the shape of the graph of the weight function, the mean curvature of the boundary and a nonlinear perturbation of lower order on the existence of solutions of problem (1.1).

Article information

Differential Integral Equations, Volume 19, Number 1 (2006), 75-90.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 35J25: Boundary value problems for second-order elliptic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Chabrowski, J. On the exterior Neumann problem with critical growth. Differential Integral Equations 19 (2006), no. 1, 75--90. https://projecteuclid.org/euclid.die/1356050533

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