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Variational and topological methods in partially ordered Hilbert spaces. (English) Zbl 0488.47034


MSC:

47J05 Equations involving nonlinear operators (general)
47F05 General theory of partial differential operators
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References:

[1] Amann, H.: Fixed point equations and nonlinear eigenvalue in ordered Banach spaces. Siam Rev.18, 620-709 (1976) · Zbl 0345.47044
[2] Nirenberg, L.: Variational and topological methods in nonlinear problems. Bull. AMS4, 267-302 (1981) · Zbl 0468.47040
[3] Lazer, A.C., McKenna, P.J.: On the number of solutions of a nonlinear Dirichlet problem. J. Math. Anal. Appl.84, 282-294 (1981) · Zbl 0496.35039
[4] Amann, H., Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa7, 539-603 (1980) · Zbl 0452.47077
[5] Chang, C.C.: Solutions of asymptotically linear operator equations via Morse theory. Comm. Pure Appl. Math.34, 693-712 (1981) · Zbl 0457.58004
[6] Struwe, M.: A note on a result of Ambrosetti and Mancini. Proc. AMS (to appear) · Zbl 0507.35032
[7] Rabinowitz, P.: Variational methods for nonlinear eigenvalue problems. CIME, pp. 141-195. Verona 1974 Rome: Cremonese 1974 · Zbl 0278.35040
[8] Amann, H.: A note on degree theory for gradient maps (to appear) · Zbl 0501.58012
[9] Schaefer, H.H.: Topological vector spaces. Graduate Texts in Mathematics 3. Berlin, Heidelberg, New York: Springer 1980 · Zbl 0435.46003
[10] Dancer, E.N.: On the ranges of certain weakly nonlinear elliptic partial differential equations. J. Math. Pur. Appl.57, 351-366 (1978) · Zbl 0394.35040
[11] Amann, H., Hess, P.: A multiplicity result for a class of elliptic boundary value problems. Proc. Roy. Soc. Edinburgh Sect. A84, 145-151 (1979) · Zbl 0416.35029
[12] Hess, P.: On multiple solutions of nonlinear elliptic eigenvalue problems. Comm. Part. Diff. Eq.6, 951-961 (1981) · Zbl 0468.35073
[13] Deimling, K.: Ordinary Differentialequations in Banach spaces. In: Lecture Notes in Mathematics, Vol. 596. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0361.34050
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