Boundary Blow–up Rates of Large Solutions for Quasilinear Elliptic Equations with Convention Terms
نویسندگان
چکیده
We use Karamata regular variation theory to study the exact asymptotic behavior of large solutions near the boundary to a class of quasilinear elliptic equations with convection terms ⎧⎨ ⎩ Δpu±|∇u|q(p−1) = b(x) f (u), x ∈Ω,
منابع مشابه
Existences and Boundary Behavior of Boundary Blow-up Solutions to Quasilinear Elliptic Systems with Singular Weights
Using the method of explosive sub and supper solution, the existence and boundary behavior of positive boundary blow up solutions for some quasilinear elliptic systems with singular weight function are obtained under more extensive conditions.
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کاملExistence of blow - up solutions for quasilinear elliptic equation with nonlinear gradient term
In this paper, we consider the quasilinear elliptic equation in a smooth bounded domain. By using the method of lower and upper solutions, we study the existence, asymptotic behavior near the boundary and uniqueness of the positive blow-up solutions for quasilinear elliptic equation with nonlinear gradient term.
متن کاملLarge Solutions for an Elliptic System of Quasilinear Equations
In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the p-Laplacian defined by ∆pu = div(|∇u|p−2∇u), p > 1, and the exponents verify a, e > p − 1, b, c > 0 and (a − p + 1)(e − p + 1) ≥ bc. We analyze positive solutions in both components, providing necessary and ...
متن کاملThe 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 کامل