On the existence of solutions of nonlinear equations
HTML articles powered by AMS MathViewer
- by Michal Feckan PDF
- Proc. Amer. Math. Soc. 124 (1996), 1733-1742 Request permission
Abstract:
Results on the existence of solutions are derived for asymptotically quasilinear, nonlinear operator equations. Applications are given to implicit nonlinear integral equations.References
- Herbert Amann, Fixed points of asymptotically linear maps in ordered Banach spaces, J. Functional Analysis 14 (1973), 162–171. MR 0350527, DOI 10.1016/0022-1236(73)90048-7
- Juha Berkovits and Vesa Mustonen, An extension of Leray-Schauder degree and applications to nonlinear wave equations, Differential Integral Equations 3 (1990), no. 5, 945–963. MR 1059342
- Klaus Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404, DOI 10.1007/978-3-662-00547-7
- M. Fečkan, Critical points of asymptotically quadratic functions, Annal. Polon. Math LXI.1 (1995), 63–76.
- M. Fečkan, Nonnegative solutions of nonlinear integral equations, Comment. Math. Univ. Carolinae (to appear).
- Michal Fe kan, An inverse function theorem for continuous mappings, J. Math. Anal. Appl. 185 (1994), no. 1, 118–128. MR 1283045, DOI 10.1006/jmaa.1994.1236
- Robert E. Gaines and Jean L. Mawhin, Coincidence degree, and nonlinear differential equations, Lecture Notes in Mathematics, Vol. 568, Springer-Verlag, Berlin-New York, 1977. MR 0637067
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Renato Guzzardi, Positive solutions of operator equations in the nondifferentiable case, Topological methods in nonlinear functional analysis (Toronto, Ont., 1982) Contemp. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1983, pp. 137–146. MR 729509, DOI 10.1090/conm/021/729509
- Arto Kittilä, On the topological degree for a class of mappings of monotone type and applications to strongly nonlinear elliptic problems, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 91 (1994), 48. MR 1263099
- M. A. Krasnosel′skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881
- W. Okrasiński, On a nonlinear convolution equation occurring in the theory of water percolation, Ann. Polon. Math. 37 (1980), no. 3, 223–229. MR 587492, DOI 10.4064/ap-37-3-223-229
- W. Okrasiński, On the existence and uniqueness of nonnegative solutions of a certain nonlinear convolution equation, Ann. Polon. Math. 36 (1979), no. 1, 61–72. MR 529307, DOI 10.4064/ap-36-1-61-72
- W. V. Petryshyn, Solvability of various boundary value problems for the equation $x''=f(t,x,x’,x'')-y$, Pacific J. Math. 122 (1986), no. 1, 169–195. MR 825230
- Jairo Santanilla, Existence of nonnegative solutions of a semilinear equation at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), no. 4, 963–971. MR 964462, DOI 10.1090/S0002-9939-1989-0964462-9
Additional Information
- Michal Feckan
- Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia
- Email: Michal.Feckan@fmph.uniba.sk
- Received by editor(s): July 8, 1994
- Received by editor(s) in revised form: November 9, 1994
- Communicated by: Jeffrey B. Rauch
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1733-1742
- MSC (1991): Primary 45M20, 47H05, 47H17
- DOI: https://doi.org/10.1090/S0002-9939-96-03339-4
- MathSciNet review: 1327010