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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

Y. Kabeya 1,

1. 

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

Received  October 2004 Revised  March 2005 Published  October 2005

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 and Continuous Dynamical Systems, 2006, 14 (1) : 117-134. doi: 10.3934/dcds.2006.14.117
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