de Figueiredo, Djairo Guedes; Ni, Wei-Ming Perturbations of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition. (English) Zbl 0429.35035 Nonlinear Anal., Theory, Methods Appl. 3, 629-634 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 33 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B50 Maximum principles in context of PDEs 35B45 A priori estimates in context of PDEs 55M25 Degree, winding number Keywords:second order linear elliptic problems; nonlinearities without Landesman- Lazer condition; nonlinear elliptic problems; maximum principle; a priori bounds; Leray-Schauder degree theory × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Krein, M. G.; Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Am. math. Soc. Transl. Ser. 1, 10, 199-325 (1962) · Zbl 0030.12902 [2] Bers, L.; John, F.; Schechter, M., Partial Differential Equations (1964), Interscience: Interscience New York · Zbl 0126.00207 [3] Landesman, E. M.; Lazer, A. C., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech., 19, 609-623 (1970) · Zbl 0193.39203 [4] Adams, R. A., Sobolev Spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101 [5] FučikKrbecMath. Z.; FučikKrbecMath. Z. [6] HessMath. Z.; HessMath. Z. · Zbl 0356.35030 [7] Friedman, A., Partial Differential Equations (1969), Holt, Rinehart & Winston: Holt, Rinehart & Winston New York · Zbl 0224.35002 [8] Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. math. J., 21, 125-146 (1971) · Zbl 0219.35037 [9] Sattinger, D. H., Topics in Stability and Bifurcation Theory (1973), Springer-Verlag: Springer-Verlag Berlin · Zbl 0268.35042 [10] Nirenberg, L., Topics in nonlinear functional analysis, Courant Inst. Math. Sci. Lecture Notes (1974) · Zbl 0286.47037 [11] Hess; Hess [12] Lazer, A. C., On Schauder’s fixed point theorem and forced second-order nonlinear oscilations, (Harris, W. A.; Sibuya, Y., Differential and Functional Equations (1967), Benjamin: Benjamin New York) · Zbl 0155.14001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.