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Topics in Critical Point Theory by Kanishka Perera, Martin Schechter

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5

Jumping nonlinearities

5.1 Introduction

Consider the equation

images

where A is as in Chapter 4 and fC(D, H) is a potential operator. Solutions of (5.1) coincide with critical points of the C1 -functional

images

where F is the potential of f with F(0) = 0.

We will first consider the solvability of (5.1) when

images

for some (a, b) ∈ ℝ2 and a bounded potential operator pC(D, H) with

We say that (5.1) is resonant at infinity if (a, b) ∈ Σ(A), otherwise it is ...

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