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T. Bartsch and M. Willem, “On an Elliptic Equation with Concave and Convex Nonlinearities,” Proceedings of the American Mathematical Society, Vol. 123, 1995, pp. 3555-3561. doi:10.1090/S0002-9939-1995-1301008-2

has been cited by the following article:

• TITLE: Existence of Weak Solutions for a Class of Quasilinear Parabolic Problems in Weighted Sobolev Space

  AUTHORS: Meilan Qiu, Liquan Mei

  KEYWORDS: Weighted Sobolev Space; Energy Estimates; Compact Imbedding; Sobolev Interpolation Inequalities

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.1A, January 30, 2013

  ABSTRACT: In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T＞0.