In this paper, the authors prove the existence of solutions for degenerate elliptic equations of the form-div(a(x)▽_p u(x)) = g(λ, x, |u|^(p-2)u) in R^N, where ▽_pu =|▽u|^(p-2)▽u and a(x) is a degenerate nonnegat...In this paper, the authors prove the existence of solutions for degenerate elliptic equations of the form-div(a(x)▽_p u(x)) = g(λ, x, |u|^(p-2)u) in R^N, where ▽_pu =|▽u|^(p-2)▽u and a(x) is a degenerate nonnegative weight. The authors also investigate a related nonlinear eigenvalue problem obtaining an existence result which contains information about the location and multiplicity of eigensolutions. The proofs of the main results are obtained by using the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality and by using a specific minimax method, but without making use of the Palais-Smale condition.展开更多
The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the c...The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied.It is proved that uh converges weakly in W0^1,1 (Ω) to the unique solution of a limit problem as h→＋∞. Moreover, explicit expressions for the limit problem are obtained.展开更多
文摘In this paper, the authors prove the existence of solutions for degenerate elliptic equations of the form-div(a(x)▽_p u(x)) = g(λ, x, |u|^(p-2)u) in R^N, where ▽_pu =|▽u|^(p-2)▽u and a(x) is a degenerate nonnegative weight. The authors also investigate a related nonlinear eigenvalue problem obtaining an existence result which contains information about the location and multiplicity of eigensolutions. The proofs of the main results are obtained by using the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality and by using a specific minimax method, but without making use of the Palais-Smale condition.
文摘The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h^2x, Duh))=f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied.It is proved that uh converges weakly in W0^1,1 (Ω) to the unique solution of a limit problem as h→＋∞. Moreover, explicit expressions for the limit problem are obtained.
