A global bifurcation result of a Neumann problem with indefinite weight

This paper is concerned with the bifurcation result of nonlinear Neumann problem \begin{equation} \left\{\begin{array}{lll} -\Delta_p u=& \lambda m(x)|u|^{p-2}u + f(\lambda,x,u)& \mbox{in} \ \Omega\\ \frac{\partial u}{\partial \nu}\hspace{0.55cm}= & 0 & \mbox{on} \ \partial\Omega. \end{array} \right. \end{equation} We prove that the principal eigenvalue $\lambda_1$ of the corresponding eigenvalue problem with $f\equiv 0,$ is a bifurcation point by using a generalized degree type of Rabinowitz

On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

We study the existence of nontrivial solutions for the problem Δu=u, in a bounded smooth domain Ω⊂ℝℕ, with a semilinear boundary condition given by ∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ∈]0,λ1];λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods

Bifurcation of nonlinear elliptic system from the first eigenvalue

We study the following bifurcation problem in a bounded domain $\Omega$ in $\mathbb{R}^N$: \left\{\begin{array}{lll} -\Delta_p u=&\lambda |u|^{\alpha}|v|^{\beta}v \,+ f(x,u,v,\lambda)& \mbox{in} \ \Omega\\ -\Delta_q v=&\lambda |u|^{\alpha}|v|^{\beta}u \, + g(x,u,v,\lambda) & \mbox{in} \ \Omega\\ (u,v)\in & W_0^{1,p}(\Omega)\times W_0^{1,q}(\Omega). & \ \end{array} \right. We prove that the principal eigenvalue $\lambda_1$ of the following eigenvalue problem \left\{\begin{array}{lll} -\Delta_p u=&\lambda |u|^{\alpha}|v|^{\beta}v \,& \mbox{in} \ \Omega\\ -\Delta_q v=&\lambda |u|^{\alpha}|v|^{\beta}u \,& \mbox{in} \ \Omega\\ (u,v)\in & W_0^{1,p}(\Omega)\times W_0^{1,q}(\Omega)& \ \end{array} \right. is simple and isolated and we prove that $(\lambda_1,0,0)$ is a bifurcation point of the system mentioned above

3D MODELS RETRIEVAL BASED ON TURNING ANGLE FUNCTION

Recent scanning technology and 3D modeling allowed having a large 3D meshes database. These models are widely used in several areas such as CAD, computer graphics and audiovisual production. Content based retrieval is a necessary solution to structure, to manage the multimedia data, and to navigate in these databases. In this paper, we propose a method to automatically search and retrieve 3D models visually similar to a query 3D model. This is based on the representation of a 3D model by a series of slices along a direction; the nearest models to the query are those which have cuts similar to it