Boundary Behavior for Solutions of Singular Quasi–linear Elliptic Equations
نویسندگان
چکیده
In this paper, for 1 γ 3 our main purpose is to consider the quasilinear elliptic equation: div(|∇u|m−2∇u) + (m− 1)u−γ = 0 on a bounded smooth domain Ω ⊂ RN , N > 1 . We get some first-order estimates of a nonnegative solution u satisfying u = 0 on ∂Ω . For γ = 1 , we find the estimate: limx→∂Ω u(x)/p(δ (x)) = 1 , where p(r) ≈ r m √ m log(1/r) near r = 0 , δ (x) denotes the distance from x to ∂Ω . For 1 < γ 3 , we obtain
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملAnalytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations
In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...
متن کاملBifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations
In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...
متن کاملNvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition
Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...
متن کاملExistence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کامل