Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition

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January 2006, 14(1): 117-134. doi: 10.3934/dcds.2006.14.117

Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition

1.	Department of Applied Mathematics, Miyazaki University, Kibana, Miyazaki, 889-2192

Received October 2004 Revised March 2005 Published October 2005

Abstract
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The blowup behaviors of solutions to a scalar-field equation with the Robin condition are discussed. For some range of the parameter, there exist at least two positive solutions to the equation. Here, the blowup rate of the large solution and the scaling properties are discussed.

Keywords: bifurcation., asymptotic behaviors, Semilinear elliptic equations.

Mathematics Subject Classification: 35J25, 35B4.

Citation: Y. Kabeya. Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition. Discrete & Continuous Dynamical Systems - A, 2006, 14 (1) : 117-134. doi: 10.3934/dcds.2006.14.117

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