Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation

2012 ◽  
Vol 104 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Lin Li ◽  
Shapour Heidarkhani
Keyword(s):  
Eigenvalue Problem ◽  
Biharmonic Equation ◽  
Three Solutions ◽  
Double Eigenvalue

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Qing-Mei Zhou ◽  
Ke-Qi Wang
Keyword(s):  
Eigenvalue Problem ◽  
Critical Points ◽  
Fractional Laplacian ◽  
Nonlinear Eigenvalue Problem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractIn this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in

scholarly journals Existence of Multiple Solutions for a Quasilinear Biharmonic Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Wu Pan ◽  
Cheng-En Yu
Keyword(s):  
Critical Points ◽  
Multiple Solutions ◽  
Biharmonic Equation ◽  
Three Solutions

Using three critical points theorems, we prove the existence of at least three solutions for a quasilinear biharmonic equation.

scholarly journals EIGENVALUE PROBLEM OF BIHARMONIC EQUATION WITH HARDY POTENTIAL

2010 ◽  
Vol 47 (6) ◽  
pp. 1123-1135
Author(s):  
Yangxin Yao ◽  
Shaotong He ◽  
Qingtang Su
Keyword(s):  
Eigenvalue Problem ◽  
Biharmonic Equation ◽  
Hardy Potential

scholarly journals Perturbations near resonance for thep-Laplacian inℝN

2002 ◽  
Vol 7 (6) ◽  
pp. 323-334 ◽  
Author(s):  
To Fu Ma ◽  
Maurício Luciano Pelicer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Principal Eigenvalue ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Laplacian Equation ◽  
Near Resonance

We study a multiplicity result for the perturbedp-Laplacian equation−Δpu−λg(x)|u|p−2u=f(x,u)+h(x) in ℝN, where1<p<Nandλis nearλ 1, the principal eigenvalue of the weighted eigenvalue problem−Δpu=λg(x)|u|p−2uinℝN. Depending on which sideλis fromλ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.

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