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
Abstract:
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, Comment. Math. Univ. Carolin, (to appear).
- 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
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 103-111
- MSC: Primary 47N20; Secondary 34B15, 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1994-1233970-X
- MathSciNet review: 1233970