If ε increases (following an increase of Ve) then, Vs = Aε increases, V- = αVs increases, ε = V+ - V- decreases The negative feedback makes the system stable: a small perturbation is balanced by the output feedback. ε remains close to 0 V. The linear behavior is possible.

Analogy : stability of a marble lying on the bottom of a cup. ε represents the distance from the equilibrium position.

Positive feedback (on the positive input) : linear behavior not sure Negative feedback (on the negative input) : linear behavior possible

NB :

when the input feedback is done on the negative input, the circuit behavior can be linear but it is not always the case (saturation, bandwidth limitations, etc.)

The essential nonlinear applications of the op-amp are the comparators.
argument is covered in the resource « The electronic comparators » by the same authors.

The remaining of this resource, then, will cover only linear applications.