1Alexandroff, A. D.. Investigations of the maximum principle. Izv. Vyss. Učebn. Zaved. Matematika 5 (1958), 126–157.
2Ambrosetti, A. and Prodi, G.. On the inversion of some differentiable mappings with singularities between Banach spaces. Ann. Mat. Pura Appl. 93 (1972), 231–246.
3Chicco, M.. Some properties of the first eigenvalue and first eigenfunction of linear second order elliptic partial differential equations in divergence form. Boll. Un. Mat. Ital. 5 (1972), 245–254.
4Dancer, E. N.. On a nonlinear elliptic boundary-value problem. Bull. Austral. Math. Soc. 12 (1975), 399–405.
5Fučík, S.. Subjectivity of operators involving linear noninvertible part and nonlinear compact perturbation. Funkcial. Ekvac. 17 (1974), 73–83.
6Fučík, S.. Nonlinear equations with noninvertible linear part. Czechoslovak Math. J. 24 (1974), 467–495.
7Fučík, S.. Further remark on a paper of E. M. Landesman and A. C. Lazer. Comment. Math. Univ. Carolinae 16 (1974), 259–271.
8Fučík, S.. Boundary value problems with jumping nonlinearities. Časopis Pěst. Mat. 101 (1976), 69–87.
9Fučík, S., Kučera, M. and Nečas, J.. Ranges of nonlinear asymptotically linear operators. J. Differential Equations 17 (1975), 375–394.
10Fučík, S. and Lovicar, V.. Boundary value and periodic problem for the equation x”(t)+g(x(t))= p(t). Comment. Math. Univ. Carolinae. 15 (1974), 351–355.
11Hess, P.. On semi-coercive nonlinear problems. Indiana Univ. Math. J. 23 (1974), 645–654.
12Krasnosel'skii, M. A.. Positive solutions of operator equations (Groningen: Noordhoff, 1964).
13Krasnosel'skii, M. A. and Lifsic, E. A.. Duality principles for boundary-value problems. Soviet Math. Dokl. 8 (1967), 1236–1239.
14Ladyzhenskaya, O. A. and Ural'tseva, N.. Linear and quasilinear elliptic equations (New York: Academic Press, 1968).
15Landesman, E. M. and Lazer, A. C.. Nonlinear perturbations of linear elliptic equations at resonance. J. Math. Mech. 19 (1970), 609–623.
16Lazer, A. C.. On Schauder's fixed point theorem and forced second-order nonlinear oscillations. J. Math. Anal. Appl. 21 (1968), 421–425.
17Lazer, A. C. and Leach, D. E.. Bounded perturbations of forced harmonic oscillators at resonance. Ann. Mat. Pura Appl. 82 (1970), 49–68.
18Nečas, J.. On the range of nonlinear operators with asymptotes which are not invertible. Comment Math. Univ. Carolinae. 14 (1973), 63–72.
19Nirenberg, L.. Topics in nonlinear functional analysis (New York: Courant Inst., 1974).
20Protter, M. and Weinberger, H.. Maximum principles in differential equations (Englewood Cliffs: Prentice-Hall, 1967).
21Riesz, F. and Sz-Nagy, B.. Functional analysis (New York: Ungar, 1955).
22Schatzman, M.. Problèmes aux limites nonlinéaires semicoercifs. C.R. Hebd. Séanc. Acad. Sci. Paris Ser. A. 275 (1972), 1305–1308.
23Schwartz, J. T.. Nonlinear functional analysis (New York: Gordon and Breach, 1969).
24Trudinger, N. S.. Linear elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa 27 (1973), 265–308.
25Williams, S. A.. A sharp sufficient condition for solution of a nonlinear elliptic boundary-value problem. J. Differential Equations 8 (1970), 580–586. Added in proof: J. L. Kazdan and F. W. Warner. (Comm. Pure Appl. Math. 28 (1975), 567–597) have independently obtained a number of results closely related to ours. In many cases, their results and ours are complementary.