On the Existence of Positive Decaying Entire Solutions for a Class of Sublinear Elliptic Equations

1988 ◽  
Vol 40 (5) ◽  
pp. 1156-1173 ◽  
Author(s):  
Yasuhiro Furusho ◽  
Takaŝi Kusano
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Equations ◽  
Early Stage ◽  
Nonlinear Elliptic Equations ◽  
Entire Solution ◽  
Entire Solutions ◽  
Nonlinear Elliptic ◽  
The Subject ◽  
Image Position ◽  
Simple Equations

In recent years there has been a growing interest in the existence and asymptotic behavior of entire solutions for second order nonlinear elliptic equations. By an entire solution we mean a solution of the elliptic equation under consideration which is guaranteed to exist in the whole Euclidean N-space RN, N ≧ 2. For standard results on the subject the reader is referred to the papers [2-7, 9-21].The study of entire solutions, which at an early stage was restricted to simple equations of the form Δu + f(x, u) = 0, x ∊ RN, Δ being the N-dimensional Laplacian, has now been extended and generalized to elliptic equations of the typeAwhere

On some nonlinear elliptic equations involving derivatives of the nonlinearity

1985 ◽  
Vol 100 (3-4) ◽  
pp. 281-294 ◽  
Author(s):  
J. Carrillo ◽  
M. Chipot
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Elliptic Boundary ◽  
Nonlinear Elliptic Equations ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Derivatives Of

SynopsisWe give some results on existence and uniqueness for the solution of elliptic boundary value problems of typewhen the βi are not necessarily smooth.

Non-existence of solutions for some nonlinear elliptic equations involving measures

2000 ◽  
Vol 130 (1) ◽  
pp. 167-187 ◽  
Author(s):  
L. Orsina ◽  
A. Prignet
Keyword(s):  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Model Problem ◽  
Nonlinear Elliptic Equations ◽  
Dirichlet Boundary Conditions ◽  
Regular Functions ◽  
Nonlinear Elliptic ◽  
Bounded Open Subset ◽  
Image Position

In this paper, we study the non-existence of solutions for the following (model) problem in a bounded open subset Ω of RN: with Dirichlet boundary conditions, where p > 1, q > 1 and μ is a bounded Radon measure. We prove that if λ is a measure which is concentrated on a set of zero r capacity (p < r ≤ N), and if q > r (p − 1)/(r − p), then there is no solution to the above problem, in the sense that if one approximates the measure λ with a sequence of regular functions fn, and if un is the sequence of solutions of the corresponding problems, then un converges to zero.We also study the non-existence of solutions for the bilateral obstacle problem with datum a measure λ concentrated on a set of zero p capacity, with u in for every υ in K, finding again that the only solution obtained by approximation is u = 0.

Solutions with multiple peaks for nonlinear elliptic equations

1999 ◽  
Vol 129 (2) ◽  
pp. 235-264 ◽  
Author(s):  
Daomin Cao ◽  
Ezzat S. Noussair ◽  
Shusen Yan
Keyword(s):  
Positive Solutions ◽  
Critical Points ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Multiple Peaks ◽  
Nonlinear Elliptic ◽  
Image Position

Solutions with peaks near the critical points of Q(x) are constructed for the problemWe establish the existence of 2k −1 positive solutions when Q(x) has k non-degenerate critical points in ℝN

Nodal vector solutions with clustered peaks for nonlinear elliptic equations in ℝ3

2016 ◽  
Vol 146 (5) ◽  
pp. 947-982
Author(s):  
Qihan He ◽  
Chunhua Wang
Keyword(s):  
Elliptic Equations ◽  
Bound States ◽  
Nonlinear Elliptic Equations ◽  
Coupling Constant ◽  
Nonlinear Elliptic ◽  
Image Position

We study the following coupled nonlinear Schr¨odinger system in ℝ3:where μ1 > 0, μ2 > 0 and β ∈ ℝ is a coupling constant. Irrespective of whether the system is repulsive or attractive, we prove that it has nodal semi-classical segregated or synchronized bound states with clustered spikes for sufficiently small ε under some additional conditions on P(x), Q(x) and β. Moreover, the number of this type of solutions will go to infinity as ε → 0+.

Decaying positive solutions to a system of nonlinear elliptic equations

2006 ◽  
Vol 136 (2) ◽  
pp. 301-320
Author(s):  
Fenfei Chen ◽  
Miaoxin Yao
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Bounded Below

In this paper, the second-order nonlinear elliptic system with α, γ < 1 and β ≥ 1, is considered in RN, N ≥ 3. Under suitable hypotheses on functions fi, gi, hi (i = 1, 2) and P, it is shown that this system possesses an entire positive solution , 0 < θ < 1, such that both u and v are bounded below and above by constant multiples of |x|2−N for all |x| ≥ 1.

Sign in / Sign up

Export Citation Format

Share Document