BLOW UP SOLUTIONS FOR 4-DIMENSIONAL SEMILINEAR ELLIPTIC PROBLEMS WITH EXPONENTIALLY DOMINATED NONLINEARITY
TAIEB OUNI *
Departement de Mathematiques, Faculte des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisie.
*Author to whom correspondence should be addressed.
In this paper we consider a biharmonic equation on a bounded domain Ω in R4 with large exponent in the nonlinear term, we study the existence of solutions having singular limits for some fourdimensional semilinear elliptic problem with exponential dominated nonlinearity and a singular source term given by Dirac masses with Navier boundary condition. In particular we show that such solutions blow up at exactly one point which is a critical point of the Robin function.
Keywords: Singular limits, Green's function, nonlinear domain decomposition method