Applications to semilinear problems
Now we give some applications of the previously discussed Morse theoretic and linking methods to the semilinear elliptic boundary value problem
where Ω is a bounded domain in ℝn, n ≥ 1 and f is a Carathéodory function on Ω × ℝ satisfying the growth condition
for some r ∈ [2, 2*) and a constant C > 0. Here
is the critical Sobolev exponent.
Weak solutions of (3.1) coincide with critical points ...