Approximation of a quasilinear elliptic equation with nonlinear boundary condition

Multiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition

In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.

Blow-up Behavior for a Quasilinear Parabolic Equation with Nonlinear Boundary Condition

In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary condition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point c...

The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Abstract. We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition −∂u/∂νA = g(·, ·, u) with a locally defined, Lr-bounded function g(t, ·, ξ). We prove the existence of a local weak solution to the problem by means of ...

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

A Spectral Method for an Elliptic Equation with a Nonlinear Neumann Boundary Condition

Abstract. Let Ω be an open, simply connected, and bounded region in Rd, d ≥ 2, that is diffeomorphic to Bd. Consider solving −∆u+ γu = 0 over Ω with the Neumann boundary condition ∂u ∂n = b (·, u). The function b is a nonlinear function of u. The problem is reformulated in a weak form, and then a spectral Galerkin method is used to create a sequence of finite dimensional nonlinear problems. An ...