Ground State Solutions for a Semilinear Problem With Critical Exponent
(2009) Differential and Integral Equations — Vol. 22, n° 9-10, p. 913-926 (2009)
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- Abstract
- This work is devoted to the existence and to qualitative properties of ground state solutions of the Dirchlet problem for the semilinear equation $-Delta u-lambda u=vert uvert^{2^*-2}u$ in a bounded domain. Here $2^*$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial solutions. We focus on the indefinite case where $lambda$ is larger than the first Dirichlet eigenvalue of the Laplacian, and we present a particularly simple approach to the study of ground states.
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Willem, M., Szulkin, A., & Weth, T. (2009). Ground State Solutions for a Semilinear Problem With Critical Exponent. Differential and Integral Equations, 22(9-10), 913-926. https://hdl.handle.net/2078.5/154761 (Original work published 2009)