On a conjecture related to the number of solutions of a nonlinear Dirichlet problem

1983 ◽  
Vol 95 (3-4) ◽  
pp. 275-283 ◽  
Author(s):  
A. C. Lazer ◽  
P. J. McKenna
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Boundary ◽  
Elliptic Boundary Value Problem ◽  
Number Of Solutions ◽  
Nonlinear Dirichlet Problem ◽  
One Dimensional ◽  
Elliptic Boundary Value ◽  
The Past ◽  
Semilinear Elliptic ◽  
The One

SynopsisIn an earlier paper (1981), the present authors made a conjecture about the number of solutions of a semilinear elliptic boundary value problem which has been investigated extensively in the past decade. The conjecture is proved in the one-dimensional case.

A Quasi-Linear Elliptic Boundary Value Problem

1966 ◽  
Vol 18 ◽  
pp. 1105-1112 ◽  
Author(s):  
R. A. Adams
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Classical Solutions ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Open Set ◽  
Image Position ◽  
Linear Elliptic Boundary ◽  
Typical Point

Let Ω be a bounded open set in Euclidean n-space, En. Let α = (α1, … , an) be an n-tuple of non-negative integers;and denote by Qm the set ﹛α| 0 ⩽ |α| ⩽ m}. Denote by x = (x1, … , xn) a typical point in En and putIn this paper we establish, under certain circumstances, the existence of weak and classical solutions of the quasi-linear Dirichlet problem1

scholarly journals Nontrivial solutions of a semilinear elliptic problem via variational methods

2004 ◽  
Vol 69 (2) ◽  
pp. 267-275 ◽  
Author(s):  
Zhi-Qing Han
Keyword(s):  
Variational Methods ◽  
Elliptic Boundary ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
At Resonance ◽  
Nonlinear Elliptic Boundary

Using variational methods, we investigate the existence of nontrivial solutions of a nonlinear elliptic boundary value problem at resonance under generalised Ahmad-Lazer-Paul conditions. Some new results are obtained and some results in the literature are improved.

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