Nonlinear PDE with vector fields
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A nonlinear PDE on a compact manifold is proposed where we use a given vector field. The nonlinear term involves the critical Sobolev exponent growth. To obtain the existence of solutions, conditions linking a critical point of the field and the scalar curvature are found. The second point is devoted to studying the viscosity limit of the solutions when the Laplacian term tends to zero.
KeywordsVector Field Scalar Curvature Minimum Point Sobolev Inequality Mountain Pass
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- B. Gidas, W.-M. Ni, and L. Nirenberg,Symmetry of Positive Solutions of Nonlinear Elliptic Equations in ℝn, Math. Anal. Appl., Part A, Advances in Math. Suppl. Studies 7A, (L. Nachbin, ed.), Academic Press, San Diego, 1981, pp. 369–402.Google Scholar
- D. Gilbarg and N. S. Trudinger,Elliptic Partial Differentiable Equations of Second Order, 2nd edn., Springer-Verlag, Berlin, 1983.Google Scholar