On a variational approximation of superlinear indefinite elliptic problems
Roberto Ferretti, Stefano Finzi Vita · Numerical Functional Analysis and Optimization · 1998
We consider finite element approximations for positive solutions of the semilinear elliptic problem with the function a(·) changing sign, and with superlinear growth (p < 1). We expect solutions of this problem to be saddle-points of the associated energy functional, and therefore minimization techniques are not suitable for this case. However, since solutions may be characterized as constrained maxima for a different functional, we will give a discrete version of this approach and study the convergence of approximate solutions. We also present some numerical experiments.