Singular perturbation of some quasilinear elliptic boundary value problems given in divergence form
نویسندگان
چکیده
منابع مشابه
On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations
We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem −div (|∇u|∇u) = λa(x)|u|u+ b(x)|u|u, x ∈ Ω, ∂u ∂n = 0, x ∈ ∂Ω , where Ω is a smooth bounded domain in Rn, b changes sign, 1 < p < N , 1 < γ < Np/(N − p) and γ 6= p. We prove that (i) if ∫ Ω a(x) dx 6= 0 and b satisfies another integral condition, then there exists some λ∗ suc...
متن کاملA Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. Ii
Let Ω ⊂ RN with N ≥ 2. We consider the equations N ∑ i=1 ui ∂2u ∂xi + p(x) = 0, u|∂Ω = 0, with a1 ≥ a2 ≥ .... ≥ aN ≥ 0 and a1 > aN . We show that if Ω is a convex bounded region in RN , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for no...
متن کاملBranches of positive and free boundary solutions for some singular quasilinear elliptic problems
We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms. © 2008 Elsevier Inc. All rights reserved.
متن کاملMultiplicity of solutions for quasilinear elliptic boundary-value problems
This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.
متن کاملExistence and Uniqueness Theorems for Singular Anisotropic Quasilinear Elliptic Boundary Value Problems
On bounded domains Ω ⊂ R2 we consider the anisotropic problems u−auxx + u−buyy = p(x, y) in Ω with a, b > 1 and u = ∞ on ∂Ω and uuxx+uuyy+q(x, y) = 0 in Ω with c, d ≥ 0 and u = 0 on ∂Ω. Moreover, we generalize these boundary value problems to space-dimensions n > 2. Under geometric conditions on Ω and monotonicity assumption on 0 < p, q ∈ Cα(Ω) we prove existence and uniqueness of positive solu...
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: Journal of Mathematical Analysis and Applications
سال: 1972
ISSN: 0022-247X
DOI: 10.1016/0022-247x(72)90237-5