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Volume 4,     Number 2,     Spring 1996

 

ASYMPTOTIC BEHAVIOR OF
SOLUTION CONTINUA FOR
SEMILINEAR ELLIPTIC PROBLEMS
STANISLAUS MAIER-PAAPE AND KLAUS SCHMITT

Abstract. We consider parameter dependent Dirichlet boundary value problems for semilinear elliptic equations whose nonlinear terms are linear at infinity. Results are presented about the asymptotic behavior of solution continua which bifurcate from infinity. In particular, we obtain the existence of infinitely many solutions in case the parameter equals a simple eigenvalue of the linearized problem.

 

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