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Topics in Critical Point Theory by Kanishka Perera, Martin Schechter

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3

Applications to semilinear problems

3.1 Introduction

Now we give some applications of the previously discussed Morse theoretic and linking methods to the semilinear elliptic boundary value problem

images

where Ω is a bounded domain in ℝn, n ≥ 1 and f is a Carathéodory function on Ω × ℝ satisfying the growth condition

images

for some r ∈ [2, 2*) and a constant C > 0. Here

images

is the critical Sobolev exponent.

Weak solutions of (3.1) coincide with critical points ...

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