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Orlicz spaces and nonlinear elliptic eigenvalue problems. (English) Zbl 0133.05301

##### Keywords:
partial differential equations
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##### References:
 [1] Melvyn S. Berger, An eigenvalue problem for quasi-linear elliptic partial differential equations, Bull. Amer. Math. Soc. 71 (1965), 171 – 175. · Zbl 0125.33602 [2] Melvyn S. Berger, An eigenvalue problem for nonlinear elliptic partial differential equations, Trans. Amer. Math. Soc. 120 (1965), 145 – 184. · Zbl 0142.08402 [3] Melvyn S. Berger, A Sturm-Liouville theorem for nonlinear elliptic partial differential equations, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1277 – 1279. · Zbl 0173.43504 [4] Felix E. Browder, Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965), 176 – 183. · Zbl 0135.15802 [5] Ju. A. Dubinskiĭ, Some imbedding theorems in Orlicz classes, Dokl. Akad. Nauk SSSR 152 (1963), 529 – 532 (Russian). [6] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415 – 426. · Zbl 0102.04302 · doi:10.1002/cpa.3160140317 · doi.org [7] M. A. Krasnosel$$^{\prime}$$skiĭ and Ja. B. Rutickiĭ, Convex functions and Orlicz spaces, Translated from the first Russian edition by Leo F. Boron, P. Noordhoff Ltd., Groningen, 1961. [8] Norman Levinson, Positive eigenfunctions for \Delta \?+\?\?(\?)=0, Arch. Rational Mech. Anal. 11 (1962), 258 – 272. · Zbl 0108.28902 · doi:10.1007/BF00253940 · doi.org [9] Norman G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717 – 721. · Zbl 0129.04002 [10] James Serrin, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247 – 302. · Zbl 0128.09101 · doi:10.1007/BF02391014 · doi.org
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