References
S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I–II, Comm. Pure Appl. Math.12 (1959), 623–727;17 (1964), 35–92.
A. Ambrosetti and P. Rabinowitz,Dual variational methods in critical point theory and applications, J. Functional Analysis14 (1973), 349–381.
M. S. Berger and L. E. Fraenkel,Global free boundary problems and the calculus of variations in the large, Lecture Notes in Mathematics503, Springer-Verlag, pp. 186–192.
L. E. Fraenkel and M. S. Berger,A global theory of steady vortex rings in an ideal fluid, Acta Math.132 (1974), 13–51.
B. Gidas, W.-M. Ni and L. Nirenberg,Symmetry and related properties via maximum principle, Comm. Math. Phys.68 (1979), 209–243.
D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977.
W.-M. Ni,Some minimax principles with applications in nonlinear elliptic boundary value problems and global vortex flow, Ph.D. Thesis, New York University, June 1979.
W.-M. Ni,Some minimax principles and their applications in nonlinear elliptic equations, J. Analyse Math.37 (1980), 248–275.
M. H. Protter and H. F. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, 1967.
P. Rabinowitz,Variational methods and nonlinear eigenvalue problems, inEigenvalues in Nonlinear Problems, C.I.M.E., 1974, pp. 141–195.
M. M. Vainberg,Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964
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Supported in part by a grant from the National Science Foundation.
The results of this paper were obtained while the author was partially supported by U. S. Army Research Office grant No. DAA-29-78-6-0127 at Courant Institute, New York University.
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Ni, WM. On the existence of global vortex rings. J. Anal. Math. 37, 208–247 (1980). https://doi.org/10.1007/BF02797686
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DOI: https://doi.org/10.1007/BF02797686