On the existence of solutions of nonlinear equations

Feckan, Michal

doi:10.1090/S0002-9939-96-03339-4

On the existence of solutions
of nonlinear equations

Author: Michal Feckan
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Results on the existence of solutions are derived for asymptotically quasilinear, nonlinear operator equations. Applications are given to implicit nonlinear integral equations.

1. Herbert Amann, Fixed points of asymptotically linear maps in ordered Banach spaces, J. Functional Analysis 14 (1973), 162–171. MR 0350527, https://doi.org/10.1016/0022-1236(73)90048-7
2. 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
3. Klaus Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404
4. M. Feckan, Critical points of asymptotically quadratic functions, Annal. Polon. Math LXI.1 (1995), 63--76.
5. M. Feckan, Nonnegative solutions of nonlinear integral equations, Comment. Math. Univ. Carolinae (to appear).
6. Michal Fečkan, An inverse function theorem for continuous mappings, J. Math. Anal. Appl. 185 (1994), no. 1, 118–128. MR 1283045, https://doi.org/10.1006/jmaa.1994.1236
7. 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
8. A. Granas, On a certain class of nonlinear mappings in Banach spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 9 (1957), 867-871. MR 19:968e
9. 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, https://doi.org/10.1090/conm/021/729509
10. 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
11. M. A. Krasnosel′skiĭ, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron, P. Noordhoff Ltd. Groningen, 1964. MR 0181881
12. 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, https://doi.org/10.4064/ap-37-3-223-229
13. 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, https://doi.org/10.4064/ap-36-1-61-72
14. 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
15. 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, https://doi.org/10.1090/S0002-9939-1989-0964462-9