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A sharper energy method for the localization of the support to some stationary Schrödinger equations with a singular nonlinearity

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  • We prove the compactness of the support of the solution of some stationary Schrödinger equations with a singular nonlinear order term. We present here a sharper version of some energy methods previously used in the literature.
    Mathematics Subject Classification: Primary: 35B45.


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  • [1]

    S. N. Antontsev, J. I. Díaz, and S. Shmarev, Energy methods for free boundary problems: Applications to nonlinear PDEs and fluid mechanics, Progress in Nonlinear Differential Equations and their Applications, 48. Birkhäuser Boston Inc., Boston, MA, 2002.


    P. Bégout and J. I. Díaz, Existence of weak solutions to some stationary Schrödinger equations with singular nonlinearity, Accepted for publication in RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., & arXiv:1304.3389.


    P. Bégout and J. I. Díaz, Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations, Submitted, & arXiv:1301.0715.


    P. Bégout and J. I. Díaz, On a nonlinear Schrödinger equation with a localizing effect, C. R. Math. Acad. Sci. Paris, 342 (2006), 459-463.doi: 10.1016/j.crma.2006.01.027.


    P. Bégout and J. I. Díaz, Localizing estimates of the support of solutions of some nonlinear Schrödinger equations - The stationary case, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 35-58.doi: 10.1016/j.anihpc.2011.09.001.


    T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10, New York University Courant Institute of Mathematical Sciences, New York, 2003.

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