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Nonlinear perturbations of linear elliptic and parabolic problems at resonance: existence of multiple solutions. (English) Zbl 0392.35051


MSC:

35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
47F05 General theory of partial differential operators
35J60 Nonlinear elliptic equations
35K55 Nonlinear parabolic equations
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References:

[1] A. Ambrosetti - G. Mancini , Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance (to appear). · Zbl 0393.35032
[2] A. Ambrosetti - G. Mancini , Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part , Ann. Scuola Norm. Sup. Pisa 5 ( 1978 ), pp. 15 - 28 . Numdam | MR 487001 | Zbl 0375.35024 · Zbl 0375.35024
[3] H. Brézis , Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Nonlinear Functional Analysis , E. Zarantonello ed., Academic Press , 1971 . MR 394323 · Zbl 0278.47033
[4] H. Brezis - L. Nirenberg , Characterizations of the ranges of some nonlinear operators and applications to boundary value problems , Ann. Scuola Norm. Sup. Pisa 5 ( 1978 ), pp. 225 - 326 . Numdam | MR 513090 | Zbl 0386.47035 · Zbl 0386.47035
[5] S Fučik - M. Krbec , Boundary value problems with bounded nonlinearity and general null-space of the linear part , Math. Z. 155 ( 1977 ), pp. 129 - 138 . Article | MR 473513 | Zbl 0337.35034 · Zbl 0337.35034
[6] P. Hess , A remark on the preceding paper of Fučik and Krbec , Math. Z. 155 ( 1977 ), pp. 139 - 141 . Article | MR 473514 | Zbl 0356.35030 · Zbl 0356.35030
[7] E.M. Landesman - A.C. Lazer , Nonlinear perturbations of linear elliptic boundary value problems at resonance , J. Math. Mech. , 19 ( 1970 ), pp. 609 - 623 . MR 267269 | Zbl 0193.39203 · Zbl 0193.39203
[8] S. Mizohata , The Theory of Partial Differential Equations , Cambridge University Press , 1973 . MR 599580 | Zbl 0263.35001 · Zbl 0263.35001
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