Boundary value problems for semilinear elliptic equations of arbitrary order in unbounded domains
نویسندگان
چکیده
منابع مشابه
Semilinear Elliptic Boundary-value Problems on Bounded Multiconnected Domains
A semilinear elliptic boundary-value problem on bounded multiconnected domains is studied. The authors prove that under suitable conditions, the problem may have no solutions in certain cases and many have one or two nonnegative solutions in some other cases. The radial solutions were also studied in annular domains.
متن کاملLiouville type results for semilinear elliptic equations in unbounded domains
This paper is devoted to the study of some class of semilinear elliptic equations in the whole space: −aij(x)∂iju(x)− qi(x)∂iu(x) = f(x, u(x)), x ∈ R . The aim is to prove uniqueness of positive bounded solutions Liouville type theorems. Along the way, we establish also various existence results. We first derive a sufficient condition, directly expressed in terms of the coefficients of the line...
متن کاملPalais-smale Approaches to Semilinear Elliptic Equations in Unbounded Domains
Let Ω be a domain in RN , N ≥ 1, and 2∗ = ∞ if N = 1, 2, 2∗ = 2N N−2 if N > 2, 2 < p < 2 ∗. Consider the semilinear elliptic problem −∆u+ u = |u|p−2u in Ω; u ∈ H 0 (Ω). Let H1 0 (Ω) be the Sobolev space in Ω. The existence, the nonexistence, and the multiplicity of positive solutions are affected by the geometry and the topology of the domain Ω. The existence, the nonexistence, and the multipli...
متن کاملDirichlet Problems for Semilinear Elliptic Equations with a Fast Growth Coefficient on Unbounded Domains
When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super an...
متن کاملExistence of Solutions for Quasilinear Elliptic Boundary Value Problems in Unbounded Domains
Under suitable assumptions we prove, via the Leray-Schauder fixed point theorem, the existence of a solution for quasilinear elliptic boundary value problem in C(Ω̄) ∩ W (Ω), q > N which satisfies in addition the condition, (1+ | x |) 1 2u ∈ C(Ω̄).
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: Rocky Mountain Journal of Mathematics
سال: 1988
ISSN: 0035-7596
DOI: 10.1216/rmj-1988-18-3-519