We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in $ℝ^N$, a is a weight function and f a nonlinear perturbation. Our approach is variational in character.
In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.
We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
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