Geodesic
Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 674-683

Voir la notice de l'article provenant de la source Cambridge University Press

We study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the nonlinear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.
DOI : 10.4153/CMB-2010-073-x
Mots-clés : 58J05, 35P30, Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions 
Kristály, Alexandru; Papageorgiou, Nikolaos S.; Varga, Csaba. Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary. Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 674-683. doi: 10.4153/CMB-2010-073-x
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[1] [1] Carslaw, H. S. and Jaeger, J. C., Conduction of heat in solids. 2nd edition, Oxford Press, 1959, pp. 17–23. Google Scholar

[2] [2] Diaz, J. I., Nonlinear partial differential equation and free boundaries. I. Elliptic equations. Research Notes in Mathematics, 106, Pitman (Advanced Publishing Program), Boston, MA, 1985. Google Scholar

[3] [3] Escobar, J. F., The Yamabe problem on manifolds with boundary. J. Differential Geom. 35(1992), no. 1, 21–84. Google Scholar

[4] [4] Escobar, J. F., Conformal deformation of Riemannian metric to a scalar flat metric with constant mean curvature on the boundary. Ann. of Math. 136(1992), no. 1, 1–50. doi:10.2307/2946545 Google Scholar

[5] [5] Escobar, J. F., Conformal metrics with prescribed mean curvature on the boundary. Calc. Var. Partial Differential Equations 4(1996), no. 6, 559–592. doi:10.1007/BF01261763 Google Scholar

[6] [6] Michalek, R., Existence of positive solution of a general quasilinear elliptic equation with a nonlinear boundary condition of mixed type. Nonlinear Anal. 15(1990), no. 9, 871–882. doi:10.1016/0362-546X(90)90098-2 Google Scholar

[7] [7] Ricceri, B., A three critical points theorem revisited. Nonlinear Anal. 70(2009), no. 9, 3084–3089. doi:10.1016/j.na.2008.04.010 Google Scholar

[8] [8] Ricceri, B., Sublevel sets and global minima of coercive functionals and local minima of their perturbations. J. Nonlinear Convex Anal. 5(2004), no. 2, 157–168. Google Scholar

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