scholarly journals ON EIGENVALUE PROBLEMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 407-419 ◽  
Author(s):  
Zhenhai Liu ◽  
Guifang Liu
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problems ◽  
Hemivariational Inequalities ◽  
Generalized Gradient ◽  
At Resonance ◽  
Quasilinear Elliptic ◽  
First Eigenfunction

AbstractThis paper is devoted to the Dirichlet problem for quasilinear elliptic hemivariational inequalities at resonance as well as at non-resonance. Using Clarke's notion of the generalized gradient and the property of the first eigenfunction, we also build a Landesman–Lazer theory in the non-smooth framework of quasilinear elliptic hemivariational inequalities.

On boundary variational–hemivariational inequalities of elliptic type

2010 ◽  
Vol 140 (2) ◽  
pp. 419-434 ◽  
Author(s):  
Zhenhai Liu
Keyword(s):  
Existence Of Solutions ◽  
Hemivariational Inequalities ◽  
Elliptic Type ◽  
Generalized Gradient ◽  
At Resonance ◽  
First Eigenfunction

This paper investigates the existence of solutions for boundary variational–hemivariational inequalities of elliptic type at resonance as well as at non-resonance. Using the notion of the generalized gradient of Clarke and the property of the first eigenfunction, we also build a Landesman–Lazer theory in the non-smooth framework of variational–hemivariational inequalities of elliptic type.

Eigenvalue problems for variational-hemivariational inequalities at resonance

1998 ◽  
Vol 33 (2) ◽  
pp. 161-180 ◽  
Author(s):  
D. Goeleven ◽  
D. Motreanu ◽  
P.D. Panagiotopoulos
Keyword(s):  
Eigenvalue Problems ◽  
Hemivariational Inequalities ◽  
At Resonance

scholarly journals Eigenvalue problems for a quasilinear elliptic equation onℝN

2005 ◽  
Vol 2005 (18) ◽  
pp. 2871-2882 ◽  
Author(s):  
Marilena N. Poulou ◽  
Nikolaos M. Stavrakakis
Keyword(s):  
Elliptic Equation ◽  
Weight Function ◽  
Quasilinear Elliptic Equation ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Laplacian Operator ◽  
Quasilinear Elliptic

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation−Δpu=λg(x)|u|p−2u,x∈ℝN,lim|x|→+∞u(x)=0, whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator and the weight functiong(x), being bounded, changes sign and is negative and away from zero at infinity.

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

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