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Brézis, Haïm; Browder, F. E.

Strongly nonlinear elliptic boundary value problems. (English) Zbl 0453.35029

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 5, 587-603 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0453.35029

Cited in 37 Documents

MSC:

35J60 Nonlinear elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
35B45 A priori estimates in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

strongly nonlinear elliptic boundary value problems; Leray-Lions conditions; growth restriction; sign condition; existence and uniqueness; null Dirichlet boundary conditions
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References:

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[2] H. Brézis , Integrates convexes dans les espaces de Sobolev , Israel Jour. Math. , 13 ( 1972 ), pp. 9 - 23 . MR 341077 | Zbl 0249.46017 · Zbl 0249.46017
[3] F.E. Browder , Existence theory for boundary value problems for quasilinear elliptic systems with strongly lower order terms , Proc. Symposia in Pure Mathematics , vol. 23 , American Mathematical Society , Providence, R. I. ( 1971 ), pp. 269 - 286 . MR 340815 | Zbl 0265.35035 · Zbl 0265.35035
[4] F.E. Browder , Pseudo-monotone’ operators and nonlinear elliptic boundary value problems on unbounded domains , Proc. Nat. Acad. Sci. , 74 ( 1977 ), pp. 2659 - 2661 . MR 445124 | Zbl 0358.35034 · Zbl 0358.35034 · doi:10.1073/pnas.74.7.2659
[5] D.E. Edmunds - V.B. Moscatelli - J.L.R. Webb , Strongly nonlinear elliptic operators in unbounded domains , Publications Math. de l’Dniversité Bordeaux I , 4 ( 1974 ), pp. 5 - 32 . Zbl 0399.47053 · Zbl 0399.47053
[6] P. Hess , A strongly nonlinear elliptic boundary value problem , Jour. Math. Analysis and Appl. , 43 ( 1973 ), pp. 241 - 249 . MR 318670 | Zbl 0267.35039 · Zbl 0267.35039 · doi:10.1016/0022-247X(73)90272-2
[7] P. Hess , On nonlinear mappings of monotone type with respect to two Banach spaces , Jour. math. pure et appl. , 52 ( 1973 ), pp. 13 - 26 . MR 636418 | Zbl 0222.47019 · Zbl 0222.47019
[8] P. Hess , Variational inequalities for strongly nonlinear elliptic operators , Jour. Math. pure et appl. , 52 ( 1973 ), pp. 285 - 298 . MR 336057 | Zbl 0259.47050 · Zbl 0259.47050
[9] I. Natanson , Theory of functions of a real variable , Ungar , New York , vol. 1 ( 1955 ). MR 67952 | Zbl 0064.29102 · Zbl 0064.29102
[10] C.G. Simader , Über schwache Losungen des Dirichletproblems für streng nichtlineäre Differentialgleichungen , Math. Zeitschrift , 150 ( 1976 ), pp. 1 - 26 . Article | MR 420001 | Zbl 0354.35039 · Zbl 0354.35039 · doi:10.1007/BF01213881
[11] J.R.L. Webb , On the Dirichlet problem for strongly nonlinear elliptic operators in unbounded domains , Jour. London Math. Soc. , II Ser., 10 ( 1975 ), pp. 163 - 170 . MR 393836 | Zbl 0316.35037 · Zbl 0316.35037 · doi:10.1112/jlms/s2-10.2.163
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