We consider the p-Laplacian in R perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p > d and p = d and discuss the connection with Sobolev interpolation inequalities. AMS Mathematics Subject Classification: 49R05, 35P30

in this paper, we try to find a particular combination of wavelet shrinkage and nonlinear diffusion for noise removal in dental images. we selected the wavelet diffusion and modified its automatic threshold selection by proposing new models for speckle related modulus. the laplacian mixture model and circular symmetric laplacian mixture models were evaluated and as it could be expected, the lat...

The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1...

We consider one dimensional p-Laplacian eigenvalue problems of the form −∆pu = (λ− q)|u|p−1sgnu, on (0, b), together with periodic or separated boundary conditions, where p > 1, ∆p is the p-Laplacian, q ∈ C1[0, b], and b > 0, λ ∈ R. It will be shown that when p 6= 2, the structure of the spectrum in the general periodic case (that is, with q 6= 0 and periodic boundary conditions), can be comple...

We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...