### Schauder's Theorem and the method of a priori bounds

#### Abstract

#### Keywords

#### References

R.G. Bartle and L.M. Graves, Mappings between function spaces, Trans. Amer. Math. Soc. 72 (1952), 400–413.

N. El Khattabi, M. Frigon and N. Ayyadi, Multiple solutions of boundary value problems with φ-Laplacian operators and under a Wintner–Nagumo growth condition, Bound. Value Probl. 2013:236 (2013), 21 pp.

N. El Khattabi, M. Frigon and N. Ayyadi, Multiple solutions of problems with nonlinear first order differential operators, J. Fixed Point Theory Appl. 17 (2015), 23–42.

A. Granas, On the Leray–Schauder alternative, Topol. Methods Nonlinear Anal. 2 (1993), 225–231.

A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, 2003.

A. Granas and Z.E.A. Guennoun, Quelques résultats dans la théorie de Bernstein–Carathéodory de l’équation y 00 = f (t, y, y 0 ), C.R. Acad. Sci. Paris Sér. I Math. 306 (1988), 703–706 (in French).

A. Granas, R.B. Guenther and J.W. Lee, On a theorem of S. Bernstein, Pacific J. Math. 74 (1978), 67–82.

A. Granas, R.B. Guenther and J.W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures Appl. (9) 70 (1991), 153–196.

J. Mawhin, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. Differential Equations 12 (1972), 610–636.

J. Mawhin, First order ordinary differential equations with several periodic solutions, Z. Angew. Math. Phys. 38 (1987), 257–265.

H. Schaefer, Ueber die Methode der a priori-Schranken, Math. Ann. 129 (1955), 415–416.

### Refbacks

- There are currently no refbacks.