Results 21 to 30 of about 455 (85)
A result on the bifurcation from the principal eigenvalue of the Ap‐Laplacian
Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 185-195, 1997., 1997 We study the following bifurcation problem in any bounded domain Ω in ℝN: . We prove that the principal eigenvalue λ1 of the eigenvalue problem is a bifurcation point of the problem mentioned above.
P. Drábek, A. Elkhalil, A. Touzani
wiley +1 more source
Lyapunov-type Inequalities for Partial Differential Equations [PDF]
, 2013 In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace ...
Juan P. Pinasco, Napoli, Pablo L. De
core +2 more sources
Continuous spectrum for some classes of (p,2)-equations with linear or sublinear growth
, 2017 We are concerned with two classes of nonlinear eigenvalue problems involving equations driven by the sum of the p-Laplace (p > 2) and Laplace operators.
Nejmeddine Chorfi +1 more
semanticscholar +1 more source
On a problem of lower limit in the study of nonresonance
Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 227-237, 1997., 1997 We prove the solvability of the Dirichlet problem for every given h, under a condition involving only the asymptotic behaviour of the potential F of f with respect to the first eigenvalue of the p‐Laplacian Δp. More general operators are also considered.
A. Anane, O. Chakrone
wiley +1 more source
Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 679-688, 1996., 1994 We consider the semilinear elliptic eigenvalue problem The asymptotic behavior of the variational eigenvalues μ = μn(r, α) obtained by Ljusternik‐Schnirelman theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that Vol(Ωr) → 0, ∞ as r → ∞.
Tetsutaro Shibata
wiley +1 more source
Positivity of the infimum eigenvalue for equations of p(x)-Laplace type in RN
Boundary Value Problems, 2013 We study the following elliptic equations with variable exponents −div(ϕ(x,|∇u|)∇u)=λf(x,u)in RN. Under suitable conditions on ϕ and f, we show the existence of positivity of the infimum of all eigenvalues for the problem above, and then give an ...
I. Kim, Yun-Ho Kim
semanticscholar +2 more sources
Advances in Nonlinear Analysis, 2018 In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λF(p,Ω){\lambda_{F}(p,\Omega)} of the anisotropic p-Laplacian ...
Della Pietra Francesco +2 more
doaj +1 more source
Exponential decay of dispersion managed solitons for vanishing average dispersion [PDF]
, 2010 We show that any $L^2$ solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the affirmative Lushnikov's conjecture of exponential decay of dispersion managed
Dirk Hundertmark +3 more
core +4 more sources
NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM *
, 2010 Nonlinear rank-one modiflcation of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical flber.
Xin Huang, Z. Bai, Yangfeng Su
semanticscholar +1 more source
Existence of an unbounded branch of the set of solutions for equations of p(x)-Laplace type
Boundary Value Problems, 2014 We are concerned with the following nonlinear problem −div(ϕ(x,|∇u|)∇u)=μ|u|p(x)−2u+f(λ,x,u,∇u)in Ω subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the p(x)-Laplacian.
Yun-Ho Kim
semanticscholar +2 more sources