Nonresonance and existence for systems of nonlinear operator equations

[1] Cardoulis, L. 2002. Existence of solutions for some semilinear elliptic systems. Rostock. Math. Kolloq., 56: 29–38.  [Google Scholar]
[2] Clément, Ph, de Figueiredo, DG and Mitidieri, EE. 1992. Positive solutions of semilinear elliptic systems. Comm. P.D.E., 17: 923–940.  [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[3] Dall’Acqua, A. 2003. Positive solutions for a class of reaction-diffusion systems. Comm. Pure Appl. Anal., 2: 65–76.  [Google Scholar]
[4] de Figueiredo, DG. 1998. “Semilinear elliptic systems”. In in Nonlinear Functional Analysis and Applications to Differential Equations (Trieste, 1997), 122–152. River Edge, NJ: World Sci. Publ..  [Google Scholar]
[5] Fleckinger, J, Hernandez, J and de Thélin, F. 1995. On maximum principles and existence of positive solutions for some cooperative systems. Diff. Int. Eq., 8: 68–85.  [Google Scholar]
[6] Rothe, F. 1981. Global existence of branches of stationary solutions for a system of reaction diffusion equations from biology. Nonlinear Anal., 5: 487–498.  [Crossref], [Google Scholar]
[7] Souto, MAS. 1995. A priori estimates and existence of positive solutions of non-linear cooperative elliptic systems. Diff. Int. Eq., 8: 1245–1258.  [Google Scholar]
[8] Muzsi, D. A theory of semilinear operator equations under nonresonance conditions. Nonlinear Funct. Anal. Appl., to appear [Google Scholar]
[9] Mawhin, J and Ward, J Jr. 1981. Nonresonance and existence for non-linear elliptic boundary value problems. Nonlinear Anal., 6: 677–684.  [Google Scholar]
[10] Mawhin, J and Ward, JR. 1982. Nonuniform nonresonance conditions at the first two eigenvalues for periodic solutions forced Lienard and Duffing equations. Rocky M. J. Math., 12: 643–654.  [Google Scholar]
[11] Perov, AI and Kibenko, AV. 1966. O a certain general method for investigation of boundary value problems. Izv. Akad. Nauk SSSR, 30: 249–264. (Russian) [Google Scholar]
[12] Precup, R. 2007. A vector version of Krasnoselskii’s fixed point theorem in cones and positive periodic solutions of non-linear systems. J. Fixed Point Theor. Appl., 2: 141–151.  [Crossref], [Web of Science ®], [Google Scholar]
[13] Mihlin, SG. 1977. Linear Partial Differential Equations, Moscow: Vysshaya Shkola. (Russian) [Google Scholar]
[14] Brezis, H. 1983. Analyse fonctionelle. Theorie et applications, Paris: Dunod.  [Google Scholar]
[15] Precup, R. 2004. Lectures on Partial Differential Equations, Cluj-Napoca: Cluj University Press. (Romanian) [Google Scholar]
[16] Precup, R. 1995. “Existence results for non-linear boundary value problems under nonresonance conditions”. In Qualitative Problems for Differential Equations and Control Theory, Edited by: Corduneanu, C. 263–273. Singapore: World Scientific.  [Google Scholar]
[17] O’Regan, D and Precup, R. 2001. Theorems of Leray-Schauder Type and Applications, Amsterdam: Gordon and Breach.  [Google Scholar]
[18] Precup, R. 2002. Methods in Nonlinear Integral Equations, Dordrecht: Kluwer.  [Crossref], [Google Scholar]
[19] Gilbarg, D and Trudinger, NS. 1983. Elliptic Partial Differential Equations of Second Order, Berlin: Springer.  [Crossref], [Google Scholar]