This is a preview of subscription content, log in via an institution to check access.
References
Barbu, V., Precupanu, Th.: Convexity and optimization in Banach spaces. Alphen a. d. Rijn: Sijthoff & Noordhoff 1978
Bers, L., John, F., Schechter, M.: Partial differential equations. Amer. Math. Soc. Colloq. Publ. Providence, R.I.: Wiley and Sons 1964
Cairns, S., Morse, M.: Critical point theory in global analysis and differential topology. New York-London: Academic Press 1969
Courant, R.: Dirichlet's principle, conformal mapping and minimal surfaces. New York: Interscience 1950
Eckhaus, W.: Asymptotic analysis of singular perturbations. Amsterdam: North Holland 1979
Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Berlin: Akademie-Verlag 1974
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin: Springer 1977
Hartmann, P., Stampacchia, G.: On some non-linear elliptic differential-functional equations. Acta Math.115, 271–310 (1966)
Heinz, E.: Unstable surfaces of constant mean curvature. Arch. Rational Mech. Anal.38, 257–267 (1970)
Klötzler, R.: Mehrdimensionale Variationsrechnung. Basel-Stuttgart: Birkhäuser 1970
Ladyzhenskaya, O.A., Ural'tseva, N.N.: Linear and quasilinear elliptic equations. New York-London: Academic Press 1968
Lewy, H.: Über die-Methode der Differenzengleichungen zur Lösung von Variations-und Randwertproblemen. Math. Ann.98, 107–124 (1928)
Lions, J.L.: Perturbations singulières dans les problémes aux limites et en contrôle optimal. Lecture Notes in Math.323. Berlin-Heidelberg-New York: Springer 1973
Morrey Jr., C.B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966
Morse, M., Tompkins, C.B.: Unstable minimal surfaces of higher topological structure. Duke Math. J.8, 350–375 (1941)
Nitsche, J.C.C.: Vorlesungen über Minimalflächen. Berlin-Heidelberg-New York: Springer 1975
Palais, R.S., Smale, S.: A generalized Morse theory. Bull. Amer. Math. Soc.70, 165–172 (1964)
Shiffman, M.: Unstable minimal surfaces with any rectifiable boundary. Proc. Nat. Acad. Sci. U.S.A.28, 103–108 (1942)
Shiffman, M.: Instability for double integral problems in the calculus of variations. Ann. of Math. (2)45, 543–576 (1944)
Ströhmer, G.: Instabile Flächen vorgeschriebener mittlerer Krümmung. Math. Z.174, 119–133 (1980)
Ströhmer, G.: Instabile Lösungen der Eulerschen Gleichungen gewisser Variationsprobleme. Arch. Rational Mech. Anal.79, 219–239 (1982)
Ströhmer, G.: Some remarks about variational problems with constraints. To appear in North Holland Euler anniversary volume edited by Th.G. Rassias
Struwe, M.: On a critical point theory for minimal surfaces spanning a wire in ℝn. Preprint 569 of SFB 72, Bonn. To appear in J. Reine Angew. Math.
Struwe, M.: On a weakened Palais-Smale condition. Preprint
Tolksdorff, P.: Regularity for a more general class of quasilinear elliptic equations. Preprint 506 of SFB 72, Bonn. To appear in J. Differential Equations
Tromba, A.: On the Morse number of embedded and non-embedded minimal immersions spanning wires on the boundary of special bodies inR 3. Preprint 517 of SFB 72, Bonn
Williams, G.H.: Lipschitz continuous solutions of nonlinear obstacle problems. Math. Z.154, 51–65 (1977)
Williams, G.H.: Nonlinear nonhomogeneous elliptic variational problems with a non-constant gradient constraint. J. Math. Pures Appl. (9)60, 213–226 (1981)
Author information
Authors and Affiliations
Additional information
This paper is a translation of part of the author's Habilitationsschrift accepted by the Mathematisch-Naturwissenschaftliche Fakultät of the Rheinisch-Westfälische Technische Hochschule
Rights and permissions
About this article
Cite this article
Ströhmer, G. Unstable solutions of the Euler equations of certain variational problems. Math Z 186, 179–199 (1984). https://doi.org/10.1007/BF01161803
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01161803