Degenerate elliptic equations

In this paper, we will extend the result of Farina to the general case a0 and look for the effect of the degeneracy on the range of the exponent p on Liouville-type theorem. It seems that the presence of the weight term |x|a makes the problem more challenging. The main difficulty is that the Grushin operator is nonautonomous. This requires suitable scaled test functions in the integral estimate.

11p tamynhan9 02-12-2020 15 2   Download

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS ˘ MIHAI MIHAILESCU Received 11 January 2005; Revised 4 July 2005; Accepted 17 July 2005 The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN . The solutions will be obtained in a subspace of the Sobolev space W 1,p (RN ). The proofs rely essentially on the Mountain Pass theorem and on Ekeland’s Variational principle. Copyright © 2006 Mihai Mih˘ ilescu.

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EIGENVALUE PROBLEMS FOR DEGENERATE NONLINEAR ELLIPTIC EQUATIONS IN ANISOTROPIC MEDIA ˘ DUMITRU MOTREANU AND VICENTIU RADULESCU ¸ Received 23 September 2004 and in revised form 26 November 2004 We study nonlinear eigenvalue problems of the type − div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality.

21p sting12 10-03-2012 46 5   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data

15p sting10 07-03-2012 42 4   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient

12p sting10 07-03-2012 54 3   Download