Differential equations with nonlinear boundary conditions

Differential equations with nonlinear boundary conditions
HTML articles powered by AMS MathViewer

by Michal Fečkan PDF

Proc. Amer. Math. Soc. 121 (1994), 103-111 Request permission

This paper shows the existence of multiple unbounded branches of solutions for certain equations via the Nielsen fixed-point theory.

References

Herbert Amann, Antonio Ambrosetti, and Giovanni Mancini, Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z. 158 (1978), no. 2, 179–194. MR 481498, DOI 10.1007/BF01320867
Jean Mawhin, Stable homotopy and ordinary differential equations with nonlinear boundary conditions, Rocky Mountain J. Math. 7 (1977), no. 3, 417–424. MR 488114, DOI 10.1216/RMJ-1977-7-3-417
L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute of Mathematical Sciences, New York University, New York, 1974. With a chapter by E. Zehnder; Notes by R. A. Artino; Lecture Notes, 1973–1974. MR 0488102
Michal Fe kan, Nielsen fixed point theory and nonlinear equations, J. Differential Equations 106 (1993), no. 2, 312–331. MR 1251856, DOI 10.1006/jdeq.1993.1110
Michal Fe kan, Multiple periodic solutions of small vector fields on differentiable manifolds, J. Differential Equations 113 (1994), no. 1, 189–200. MR 1296167, DOI 10.1006/jdeq.1994.1120

Multiple perturbed solutions near nondegenerate manifolds

Robert F. Brown, Topological identification of multiple solutions to parametrized nonlinear equations, Pacific J. Math. 131 (1988), no. 1, 51–69. MR 917865, DOI 10.2140/pjm.1988.131.51
Robert F. Brown, The Lefschetz fixed point theorem, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0283793
John Tavantzis, Topological methods for finding nontrivial solutions of elliptic boundary value problems, Nonlinear Anal. 1 (1976/77), no. 6, 633–649. MR 602537, DOI 10.1016/0362-546X(77)90023-2
J. Mawhin and K. P. Rybakowski, Continuation theorems for semilinear equations in Banach spaces: a survey, Nonlinear analysis, World Sci. Publishing, Singapore, 1987, pp. 367–405. MR 934110
E. N. Dancer, On the existence of zeros of perturbed operators, Nonlinear Anal. 7 (1983), no. 7, 717–727. MR 707080, DOI 10.1016/0362-546X(83)90028-7