Existence of solution to a critical equation with variable exponent
نویسندگان
چکیده
منابع مشابه
Existence 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 کاملExistence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces
Abstract: This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent vt + div(|∇4v|p(x)−2∇4v) − |4v|q(x)−24v = g(x, v). By applying Leray-Schauder’s fixed point theorem, the existence of weak solutions of the elliptic problem is given. Furthermore, the semi-discrete method...
متن کاملGlobal Solution Branch and Morse Index Estimates of a Semilinear Elliptic Equation with Super-critical Exponent
We consider the nonlinear eigenvalue problem (0.1) { −Δu = up + λu in B, u > 0 in B, u = 0 on ∂B, where B denotes the unit ball in RN , N ≥ 3, λ > 0 and p > (N + 2)/(N − 2). According to classical bifurcation theory, the point (μ1, 0) is a bifurcation point from which emanates an unbounded branch C of solutions (λ, u) of (0.1), where μ1 is the principal eigenvalue of −Δ in B with Dirichlet boun...
متن کاملExistence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in R
Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in RN . These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superf...
متن کاملExistence of solutions for elliptic systems with critical Sobolev exponent ∗
We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2012
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2012.3743