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The aim of this paper is to establish the existence of the principal eigencurve of the p-Laplacian operator with the nonconstant weight subject to Neumann boundary conditions. We then study the nonresonce phenomena under the first eigenvalue and under the principal eigencurve, thus we obtain existence results for some nonautonomous Neumann elliptic problems involving the p-Laplacian operator.

In this article, we study the existence of the eigencurves for a Steklov problem and we obtain their variational formulation. Also we prove the simplicity and the isolation results of each point of the principal eigencurve. Also we obtain the continuity and the differentiability of the principal eigencurve.

In this paper, we show that for each $lambda in mathbb{R}$, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem $$displaylines{ Delta_pu=|u|^{p-2}u quad hbox{in } Omegacr | abla u|^{p-2}frac{partial u}{partial u}=lambda ho(x)|u|^{p-2}u+mu|u|^{p-2}u quad hbox{on } partial Omega,; }$$ also we show that the first eigenvalue is simple and isolated. Some results about their variation, density, and continuous dependence on the parameter $lambda$ are obtained.

In this work, we study the existence of the principal eigencurves for a Steklov problem with an indefinite weight for homogeneous perturbation of the p-Laplacian operator. We then establish many properties of these eigencurves: continuity, differentiability and asymptotic behaviors. We also use our approach to get similar result when mixed Dirichlet-Steklov boundary condition is considered. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of the eigencurves for a Steklov problem and we obtain their variational formulation. Also we prove the simplicity and the isolation results of each point of the principal eigencurve. Also we obtain the continuity and the differentiability of the principal eigencurve. [ABSTRACT FROM AUTHOR]

In this paper, we show that for each &lambd; ∈ ℝ, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem Δpu = |u|p-2u in Ω |∇u|p-2 ∂u/∂v = λρ(x)|u|p-2u + μ|u|p-2u on ∂Ω; also we show that the first eigenvalue is simple and isolated. Some results about their variation, density, and continuous dependence on the parameter λ are obtained. [ABSTRACT FROM AUTHOR]