p-Laplacian problems with critical Sobolev exponent
نویسنده
چکیده
We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملThe fibering map approach to a quasilinear degenerate p(x)-Laplacian equation
By considering a degenerate $p(x)-$Laplacian equation, a generalized compact embedding in weighted variable exponent Sobolev space is presented. Multiplicity of positive solutions are discussed by applying fibering map approach for the corresponding Nehari manifold.
متن کاملOn a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian and its applications
We present a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian, which is an extension of the classic identity for the ordinary Laplace. Also, some applications of our results in Sobolev spaces with variable exponent are suggested.
متن کاملExistence of solution to a critical trace equation with variable exponent
In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)−Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration–compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain...
متن کاملThree solutions to a p(x)-Laplacian problem in weighted-variable-exponent Sobolev space
In this paper, we verify that a general p(x)-Laplacian Neumann problem has at least three weak solutions, which generalizes the corresponding result of the reference [R. A. Mashiyev, Three Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent, Arab. J. Sci. Eng. 36 (2011) 1559-1567].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Asymptotic Analysis
دوره 73 شماره
صفحات -
تاریخ انتشار 2011