Multiplicity results for a fourth-order semilinear elliptic problem

1998 ◽  
Vol 31 (7) ◽  
pp. 895-908 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia
Keyword(s):  
Fourth Order ◽  
Elliptic Problem ◽  
Multiplicity Results ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

scholarly journals On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem

2005 ◽  
Vol 2005 (6) ◽  
pp. 673-683
Author(s):  
Aixia Qian ◽  
Shujie Li
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Minimax Theory ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

By means of Minimax theory, we study the existence of one nontrivial solution and multiple nontrivial solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.

Critical semilinear biharmonic equations in RN

1992 ◽  
Vol 121 (1-2) ◽  
pp. 139-148 ◽  
Author(s):  
Ezzat S. Noussair ◽  
Charles A. Swanson ◽  
Yang Jianfu
Keyword(s):  
Fourth Order ◽  
Elliptic Problem ◽  
Critical Sobolev Exponent ◽  
Sobolev Embedding ◽  
Biharmonic Equations ◽  
Best Constant ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Sobolev Exponent ◽  
Image Position

SynopsisAn existence theorem is obtained for a fourth-order semilinear elliptic problem in RN involving the critical Sobolev exponent (N + 4)/(N − 4), N>4. A preliminary result is that the best constant in the Sobolev embedding L2N/(N–4) (RN) is attained by all translations and dilations of (1 + ∣x∣2)(4-N)/2. The best constant is found to be

Existence and multiplicity results for a semilinear elliptic problem

2019 ◽  
Vol 475 (2) ◽  
pp. 1493-1501 ◽  
Author(s):  
Alfonso Castro ◽  
Jorge Cossio ◽  
Sigifredo Herrón ◽  
Carlos Vélez
Keyword(s):  
Elliptic Problem ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

NONNEGATIVE SOLUTIONS FOR INDEFINITE SUBLINEAR ELLIPTIC PROBLEMS

2012 ◽  
Vol 14 (03) ◽  
pp. 1250021 ◽  
Author(s):  
FRANCISCO ODAIR DE PAIVA
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Solution Method ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Nonnegative Solutions ◽  
Carathéodory Function ◽  
Multiplicity Of Positive Solutions

This paper is devoted to the study of existence, nonexistence and multiplicity of positive solutions for the semilinear elliptic problem [Formula: see text] where Ω is a bounded domain of ℝN, λ ∈ ℝ and g(x, u) is a Carathéodory function. The obtained results apply to the following classes of nonlinearities: a(x)uq + b(x)up and c(x)(1 + u)p (0 ≤ q < 1 < p). The proofs rely on the sub-super solution method and the mountain pass theorem.

Decaying Solutions Of 2mth Order Elliptic Problems

1991 ◽  
Vol 43 (3) ◽  
pp. 449-460 ◽  
Author(s):  
W. Allegretto ◽  
L. S. Yu
Keyword(s):  
Positive Solution ◽  
Elliptic Problem ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Weighted Spaces ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Regularity Estimates ◽  
Open Question

AbstractWe consider a semilinear elliptic problem , (n > 2m). Under suitable conditions on f, we show the existence of a decaying positive solution. We do not employ radial arguments. Our main tools are weighted spaces, various applications of the Mountain Pass Theorem and LP regularity estimates of Agmon. We answer an open question of Kusano, Naito and Swanson [Canad. J. Math. 40(1988), 1281-1300] in the superlinear case: , and improve the results of Dalmasso [C. R. Acad. Sci. Paris 308(1989), 411-414] for the case .

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