In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a cla...In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.展开更多
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
文摘In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.
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.
