Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction $f:\Omega \times E\to 2^F$, denote by $N_f\left(x\right)$ the set of all measurable selections of the multifunction $f(·,x\left(·\right)):\Omega \to 2^F$, s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator $N_f$ mapping some open domain G ⊂ X into $2^Y$, where X and Y are Köthe-Bochner...

In this survey we collect several results concerning S-type bifurcation curves for the number of solutions of reaction-diffusion stationary equations. In particular, we recall several results in the literature for the case of stationary energy balance models.