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This work reviews some basic features on the second (first nontrivial) eigenvalue λ2 to the Neumann problem ... where Ω is a bounded Lipschitz domain of RN, is the outer unit normal, and ∆pu = div(∇) is the p-Laplacian operator. We are mainly concerned with the variational characterization of &#955;2 and place emphasis on the range 1 < p < 2, where the nonlinearity |∆| becomes non smooth. We also address the corresponding result for the p-Laplacian in graphs. [ABSTRACT FROM AUTHOR]

We study a Neumann boundary-value problem on the half line for a second order equation, in which the nonlinearity depends on the (unknown) Dirichlet boundary data of the solution. An existence result is obtained by an adapted version of the method of upper and lower solutions, together with a diagonal argument.

We study a Neumann boundary-value problem on the half line for a second order equation, in which the nonlinearity depends on the (unknown) Dirichlet boundary data of the solution. An existence result is obtained by an adapted version of the method of upper and lower solutions, together with a diagonal argument. [ABSTRACT FROM AUTHOR]