Asian Journal of Mathematics and Computer Research

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.

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Abstract

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

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