5

Jumping nonlinearities

**5.1 Introduction**

Consider the equation

where *A* is as in Chapter 4 and *f* ∈ *C*(*D*, *H*) is a potential operator. Solutions of (5.1) coincide with critical points of the *C*^{1} -functional

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

We will first consider the solvability of (5.1) when

for some (*a*, *b*) ∈ ℝ^{2} and a bounded potential operator *p* ∈ *C*(*D*, *H*) with

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

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