A scalar-field type equation with the Robin condition is discussed. For some range of the parameter, the multiplicity of solutions is obtained. Moreover, one of the obtained solutions has a blowup property and the blowup point is determined.
"Multiplicity of solutions to a scalar-field equation involving the Sobolev critical exponent with the Robin condition." Adv. Differential Equations 10 (10) 1111 - 1129, 2005.