REFERENCES
[1] A. K. Abdulazizov, E. De Pascale, P. P. Zabrejko, Bohl’s theorem on bounded solutions: Infinite
systems of ordinary differential equations, Rend. Sci. Math. Appl. A 128 (1995), 37-52.
[2] J. Appell, A. Buic˘a, Numerical ranges for pairs of operators, duality mappings with gauge
function, and spectra of nonlinear operators, Mediterranean J. Math. 3 (2006), 1-13.
[3] J. Appell, A. Carbone, E. De Pascale, A note on the existence and uniqueness of H¨older solutions
of nonlinear singular integral equations, Zeitschr. Anal. Anwend. 11, 3 (1992), 377-384.
[4] J. Appell, E. De Pascale, Su alcuni parametri connessi con la misura di non compattezza di
Hausdorff in spazi di funzioni misurabili, Boll. Unione Mat. Ital. B 3 (1984), 497-515.
[5] J. Appell, E. De Pascale, Th´eor`emes de bornage pour l’op´erateur de Nemyckii dans les espaces
id´eaux, Canad. J. Math. 38, 6 (1986), 1281-1299.
[6] J. Appell, E. De Pascale, Lipschitz and Darbo conditions for the superposition operator in some
non-ideal spaces of smooth functions, Annali Mat. Pura Appl. 158 (1991), 205-217.
[7] J. Appell, E. De Pascale, O. W. Diallo, La fonction de Green pour des ´equations int´egrodiff´erentielles
de type Barbachine, Rend. Sci. Mat. Appl. 127, 2 (1993), 149-159.
[8] J. Appell, E. De Pascale, N. A. Evkhuta, P. P. Zabrejko, On the two-step Newton method for
the solution of nonlinear operator equations, Math. Nachr. 172 (1995), 5-14.
[9] J. Appell, E. De Pascale, A. S. Kalitvin, P. P. Zabrejko, On the application of the NewtonKantorovich
method to nonlinear partial integral equations, Zeitschr. Anal. Anwend. 15, 2
(1996), 397-418.
[10] J. Appell, E. De Pascale, Ju. V. Lysenko, P. P. Zabrejko, New results on Newton-Kantorovich
approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18, 1 (1997), 1-17.
[11] J. Appell, E. De Pascale, H. T. Nguyen, P. P. Zabrejko, Nonlinear integral inclusions of Hammerstein
type, Topol. Methods Nonlin. Anal. 5 (1995), 111-124.
[12] J. Appell, E. De Pascale, H. T. Nguyen, P. P. Zabrejko, Multivalued superpositions, Diss. Math. 464 (1995), 1-59.
[13] J. Appell, E. De Pascale, A. Vignoli, A comparison of different spectra for nonlinear operators,
Nonlin. Anal. TMA 40, 1 (2000), 73-90.
[14] J. Appell, E. De Pascale, A. Vignoli, A semilinear Furi-Martelli-Vignoli spectrum, Zeitschr.
Anal. Anwend. 20, 3 (2001), 565-577.
[15] J. Appell, E. De Pascale, A. Vignoli, Nonlinear Spectral Theory, DeGruyter Series Nonlin.
Anal. Appl. 10, DeGruyter, Berlin 2004.
[16] J. Appell, E. De Pascale, P. P. Zabrejko, An application of B. N. Sadovskij’s fixed point principle
to nonlinear singular equations, Zeitschr. Anal. Anwend. 6 (1987), 193-208.
[17] J. Appell, E. De Pascale, P. P. Zabrejko, Multivalued superposition operators,
Rend. Sem. Mat. Univ. Padova 86 (1991), 213-231.
[18] J. Appell, E. De Pascale, P. P. Zabrejko, On the application of the Newton-Kantorovich method
to nonlinear integral equations of Uryson type, Numer. Funct. Anal. Optim. 12, 3 (1991), 271- 283.
[19] J. Appell, E. De Pascale, P. P. Zabrejko, On the application of the method of successive approximations
and the Newton-Kantorovich method to nonlinear functional-integral equations,
Adv. Math. Sci. Appl. 2, 1 (1993), 25-38
[20] J. Appell, E. De Pascale, P. P. Zabrejko, Some remarks on Banach limits, Atti Sem. Mat. Fis.
Univ. Modena 42, 1 (1994), 273-278.
[21] J. Appell, E. De Pascale, P. P. Zabrejko, Convergence of the Newton-Kantorovich method under
Vertgejm conditions: A new improvement, Zeitschr. Anal. Anwend. 17, 2 (1998), 271-280.
[22] J. Appell, E. De Pascale, P. P. Zabrejko, On the unique solvability of Hammerstein integral
equations with non-symmetric kernels, Progr. Nonlin. Diff. Equ. 40 (2000), 27-34.
[23] V. Bur´yˇskov´a, Some properties of nonlinear adjoint operators, Rocky Mount. J. Math. 28 (1998), 41-59.
[24] D. Caponetti, E. De Pascale, P. P. Zabrejko, On the Newton-Kantorovich method in K-normed
linear spaces, Rend. Circ. Mat. Palermo 49 (2000), 545-560.
[25] Y. J. Cheng, H¨older continuity of the inverse of the p-Laplacian, J. Math. Anal. Appl. 221
(1998), 734-748.
[26] G. Chiaselotti, E. De Pascale, G. Marino, Nonlinear contractions in (o)-E-metric spaces, Rend.
Circ. Mat. Palermo II 33 (1993), 249-257.
[27] F. Cianciaruso, A further journey in the “terra incognita” of the Newton-Kantorovich method,
Nonlin. Funct. Anal. Appl. (to appear).
[28] F. Cianciaruso, E. De Pascale, Discovering the algebraic structure on the metric injective envelope
of a real Banach space, Topology Appl. 78, 3 (1997), 285-292.
[29] F. Cianciaruso, E. De Pascale, The Hausdorff measure of non hyperconvexity, Atti Sem. Mat.
Fis. Univ. Modena 47, 1 (1999), 261-267.
[30] F. Cianciaruso, E. De Pascale, The Newton-Kantorovich approximations for nonlinear integrodifferential
equations of mixed type, Ric. Mat. 51, 2 (2002), 1-12.
[31] F. Cianciaruso, E. De Pascale, Newton-Kantorovich approximations when the derivative is
H¨olderian: Old and new results, Numer. Funct. Anal. Optim. 24, 7 (2003), 713-723.
[32] F. Cianciaruso, E. De Pascale, Estimates of majorizing sequences in the Newton-Kantorovich
method, Numer. Funct. Anal. Optim. 27, 5 (2006), 529-538.
[33] F. Cianciaruso, E. De Pascale, Estimates of majorizing sequences in the Newton-Kantorovich
method: A further improvement, J. Math. Anal. Appl. 322 (2006), 329-335.
[34] F. Cianciaruso, E. De Pascale, P. P. Zabrejko, Some remarks on the Newton-Kantorovich approximations,
Atti Sem. Mat. Fis. Univ. Modena 48, 1 (2000), 207-215.
[35] G. Conti, E. De Pascale, The numerical range in the nonlinear case, Boll. Unione Mat. Ital. B
15 (1978), 210-216.
[36] G. Conti, E. De Pascale, A remark on surjectivity of quasi-bounded P-compact maps, Rend.
Ist. Mat. Univ. Trieste 8 (1977), 167-171.
[37] C. T. Cremins, G. Infante, A semilinear A-spectrum, Discrete Cont. Dynam. Systems 1, 2
(2008), 235-242.
[38] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Math. Univ.
Padova 24 (1955), 84-92.
[39] E. De Pascale, A finite dimensional reduction of the Schauder conjecture, Comm. Math. Univ.
Carolinae 34, 3 (1993), 401-404.
[40] E. De Pascale, L. De Pascale, Fixed points for some non-obviously contractive operators, Proc.
Amer. Math. Soc. 130, 11 (2002), 3249-3254.
[41] E. De Pascale, R. Guzzardi, On boundary conditions and fixed points for α-nonexpansive multivalued
mappings, Atti Accad. Naz. Lincei 58 (1975), 110-116.
[42] E. De Pascale, R. Guzzardi, On the boundary value dependence for the topological degree of
multivalued noncompact maps, Boll. Unione Mat. Ital. A 13 (1976), 110-116.
[43] E. De Pascale, R. Guzzardi, Positive fixed points and bifurcation for non-differentiable maps,
Pubbl. Dip. Mat. Univ. Calabria 14 (1983), 1-14.
[44] E. De Pascale, R. Iannacci, Periodic solutions of generalized Lienard equations with delay, Proc.
Equadiff. Conf. W¨urzburg, Lect. Notes Math. 1017 (1983), 148-156.
[45] E. De Pascale, G. Lewicki, G. Marino, Some conditions for compactness in BC(Q) and their
application to boundary value problems, Analysis 22, 1 (2002), 21-32.
[46] E. De Pascale, G. Marino, On the proof of the abstract Cauchy-Kowalewskaya type theorems:
Some improvements, Dyn. Systems Appl. 3, 2 (1994), 259-266.
[47] E. De Pascale, G. Marino, G. Metafune, On the method of backward steps by Carath´eodoryTonelli,
Zeitschr. Anal. Anw. 16, 3 (1996), 765-770.
[48] E. De Pascale, G. Marino, P. Pietramala, The use of the E-metric spaces in the search for fixed
points, Matematiche (Catania) 48, 2 (1993), 367-376.
[49] E. De Pascale, P. L. Papini, Cones and projections onto subspaces in Banach spaces, Boll.
Unione Mat. Ital. A 3 (1984), 411-420.
[50] E. De Pascale, N. Shirokonova, P. P. Zabrejko, New solvability conditions of Ljapunov-Schmidt
integral equations [in Russian], Dokl. Akad. Nauk BSSR 44, 3 (2000), 14-17.
[51] E. De Pascale, G. Trombetta, Un criterio di compattezza e la misura di noncompattezza di
Hausdorff per sottoinsiemi dello spazio delle funzioni misurabili, Rend. Sem. Mat. Fis. Milano 53 (1983), 149-151.
[52] E. De Pascale, G. Trombetta, A compactness criterion and the Hausdorff measure of noncompactness
for subsets of the space of measurable functions, Ric. Mat. 33 (1984), 133-143.
[53] E. De Pascale, G. Trombetta, Un approccio al grado topologico per applicazioni debolmente
continue in spazi di Banach riflessivi, Le Matematiche 39 (1984), 121-132.
[54] E. De Pascale, G. Trombetta, Confronto tra i gradi topologici di Canfora-Pacella e di BrowderPetryshyn,
Rend. Circ. Mat. Palermo II 12 (1986), 213-217.
[55] E. De Pascale, G. Trombetta, Fixed points and best approximations for convexly condensing
functions in topological vector spaces, Rend. Mat. Appl. 11 (1991), 175-186.
[56] E. De Pascale, G. Trombetta, A theorem on best approximations in topological vector spaces,
Proc. NATO Conf. Approx. Theory, Kluwer 1992, 351-355.
[57] E. De Pascale, G. Trombetta, Sui sottoinsiemi finitamente compatti di S(Ω), Boll. Unione Mat.
Ital. A 8 (1994), 243-249.
[58] E. De Pascale, G. Trombetta, H. Weber, Convexly totally bounded sets. Solution of a problem
of Idzik, Annali Sc. Norm. Sup. Pisa 20, 3 (1993), 341-355. 476 J. APPELL
[59] E. De Pascale, P. P. Zabrejko, Il teorema di Bohl sulle soluzioni limitate per i sistemi di infinite
equazioni differenziali ordinarie, Rend. Sci. Mat. Appl. 128 (1994), 1-16.
[60] E. De Pascale, P. P. Zabrejko, New convergence criteria for the Newton-Kantorovich method
and applications to nonlinear integral equations, Rend. Sem. Mat. Univ. Padova 100 (1998), 211-230.
[61] E. De Pascale, P. P. Zabrejko, The chord method in Banach spaces, Nonlin. Funct. Anal. Appl.
7, 4 (2002), 659-671.
[62] E. De Pascale, P. P. Zabrejko, Fixed point theorems for operators in spaces of continuous functions,
Fixed Point Theory 5, 1 (2004), 117-129.
[63] W. Feng, A new spectral theory for nonlinear operators and its applications, Abstr. Appl. Anal. 2 (1997), 163-183.
[64] W. Feng, J. R. L. Webb, A spectral theory for semilinear operators and its applications, in
Progr. Nonlin. Diff. Equ. Appl. 40, Birkh¨auser, Basel 2000, 149-163.
[65] M. Furi, M. Martelli, A. Vignoli, Contributions to the spectral theory for nonlinear operators
in Banach spaces, Annali Mat. Pura Appl. 128 (1978), 229-294.
[66] M. Furi, A. Vignoli, A nonlinear spectral approach to surjectivity in Banach spaces, J. Funct. Anal. 20 (1975), 304-318.
[67] G. Infante, J. R. L. Webb, A finite-dimensional approach to nonlinear spectral theory, Nonlin. Anal. TMA 51, 1 (2002), 171-188.
[68] J. R. Isbell, Three remarks on injective envelopes, J. Math. Anal. Appl. 27, (1969), 516-518.
[69] M. A. Krasnosel’skij, On the continuity of the operator F u(x) = f(x, u(x)) [in Russian], Doklady
Akad. Nauk SSSR 77, 2 (1951), 185-188.
[70] P. Lindqvist, On the equation div (|∇u| p−2∇u) + λ|u| p−2u = 0, Proc. Amer. Math. Soc. 109, 2 (1990), 157-163.
[71] J. L. Lions, Quelques M´ethodes de R´esolution des Probl`emes aux Limites Non Lin´eaires, Gauthier
Villars, Paris 1969
[72] B. Lou, Fixed points for operators in a space of continuous functions and applications, Proc.
Amer. Math. Soc. 127, 8 (1999), 2259-2264.
[73] I. J. Maddox, A. W. Wickstead, The spectrum of uniformly Lipschitz mappings, Proc. Royal
Irish Acad. Sect. A 89 (1989), 101-114.
[74] G. Minty, Monotone nonlinear operators in Hilbert space, Duke Math. J. 29 (1962), 341-346.
[75] B. N. Sadovskij, On a fixed point principle [in Russian], Funkt. Anal. Prilozh. 1, 2 (1967), 74-76.
[76] H. Weber, Ein ϕ-asymptotisches Spektrum und Surjektivit¨atss¨atze vom Fredholm-Typ f¨ur nichtlineare
Operatoren mit Anwendungen, Math. Nachr. 117 (1984), 7-35.
[77] E. H. Zarantonello, The closure of the numerical range contains the spectrum, Pacific J. Math. 22 (1967), 575-595.
[78] E. H. Zarantonello, Proyecciones sobre conjuntos convexos en el espacio de Hilbert y teor´ıa
espectral, Revista Uni´on Mat. Argentina 26 (1972), 187-201.
[79] E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed Point Theorems, Springer, Berlin 1991.
[80] E. Zeidler, Nonlinear Functional Analysis and its Applications II/B: Nonlinear Monotone Operators, Springer, Berlin 1991.