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Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces. (English) Zbl 1185.35113
Summary: We study the existence of radial solutions for Neumann problems in a ball and in an annular domain, associated to mean curvature operators in Euclidean and Minkowski spaces. Our approach relies on the Leray-Schauder degree together with some fixed point reformulations of our nonlinear Neumann boundary value problems

MSC:
35J93 Quasilinear elliptic equations with mean curvature operator
35J25 Boundary value problems for second-order elliptic equations
47N20 Applications of operator theory to differential and integral equations
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[1] Amann, Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z. 158 pp 179– (1978) · Zbl 0368.35032
[2] Bartnik, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys. 87 pp 131– (198283) · Zbl 0512.53055
[3] Bereanu, Radial solutions for some nonlinear problems involving mean curvature operators in Euclidean and Minkowski spaces, Proc. Amer. Math. Soc. 137 pp 171– (2009) · Zbl 1161.35024
[4] C. Bereanu, P. Jebelean, and J. Mawhin, Radial solutions for systems involving mean curvature operators in Euclidean and Minkowski spaces, AIP Conf. Proc., accepted. · Zbl 1161.35024
[5] Bereanu, Boundary-value problems with non-surjective -Laplacian and one-sided bounded nonlinearity, Adv. Differential Equations 11 pp 35– (2006) · Zbl 1111.34016
[6] Bereanu, Existence and multiplicity results for some nonlinear problems with singular -Laplacian, J. Differential Equations 243 pp 536– (2007) · Zbl 1148.34013
[7] Calabi, Examples of Bernstein problems for some nonlinear equations, Proc. Sympos. Pure Math. 15 pp 223– (1970) · Zbl 0211.12801
[8] Cheng, Maximal spacelike hypersurfaces in the Lorentz-Minkowski spaces, Ann. of Math. (2) 104 pp 407– (1976)
[9] Clément, On a modified capillary equations, J. Differential Equations 124 pp 343– (1996) · Zbl 0841.34038
[10] C. De Coster, and P. Habets, Two-point Boundary Value Problems. Lower and Upper Solutions (Elsevier, Amsterdam, 2006). · Zbl 1330.34009
[11] K. Deimling, Nonlinear Functional Analysis (Springer, Berlin, 1985). · Zbl 0559.47040
[12] García-Huidobro, Positive radial solutions of quasilinear elliptic partial differential equations in a ball, Nonlinear Anal. 35 pp 175– (1999) · Zbl 0924.35047
[13] García-Huidobro, On the structure of positive radial solutions to an equation containing a p -Laplacian with weight, J. Differential Equations 223 pp 51– (2006) · Zbl 1170.35404
[14] Hai, Existence and uniqueness for a class of quasilinear elliptic boundary value problems, J. Differential Equations 193 pp 500– (2003) · Zbl 1042.34045
[15] Kazdan, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 pp 567– (1975) · Zbl 0325.35038
[16] Mawhin, Leray-Schauder degree: a half century of extensions and applications, Topol. Methods Nonlinear Anal. 14 pp 195– (1999) · Zbl 0957.47045
[17] Mawhin, Boundary value problems for nonlinear perturbations of singular -Laplacians, Progr. Nonlinear Differential Equations Appl. 75 pp 247– (2007)
[18] Mawhin, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations, J. Differential Equations 52 pp 264– (1984) · Zbl 0557.34036
[19] de Queiroz, A Neumann problem with logarithmic nonlinearity in a ball, Nonlinear Anal. 70 pp 1656– (2009) · Zbl 1170.35427
[20] Torres, Periodic oscillations of the relativistic pendulum with friction, Phys. Lett. A 372 pp 6386– (2008) · Zbl 1225.70010
[21] Treibergs, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent. Math. 66 pp 39– (1982) · Zbl 0483.53055
[22] Zhang, Existence of solutions for weighted p (r)-Laplacian systems boundary value problems, J. Math. Anal. Appl. 327 pp 127– (2007)
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