The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit $p\to \infty $

Convergence of the Allen-cahn Equation with Neumann Boundary Conditions

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke’s mean curvature flow with a generalized right angle condition on the boundary.

Variational Method to the Impulsive Equation with Neumann Boundary Conditions

We study the existence and multiplicity of classical solutions for second-order impulsive SturmLiouville equation with Neumann boundary conditions. By using the variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions, and infinitely many solutions under some different conditions, respectively. Some ...

EXISTENCE OF SOLUTIONS FOR p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MULTI-POINT NONLINEAR NEUMANN BOUNDARY CONDITIONS AT RESONANCE

This work concerns the multi-point nonlinear Neumann boundaryvalue problem involving a p-Laplacian-like operator (φ(u′))′ = f(t, u, u′), t ∈ (0, 1), u′(0) = u′(η), φ(u′(1)) = m X

LOCAL AND NONLOCAL WEIGHTED p-LAPLACIAN EVOLUTION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

Blow-up phenomena for p-Laplacian parabolic problems with Neumann boundary conditions

where p > 2 and is a bounded domain in Rn (n≥ 2) with smooth boundary ∂ . By introducing some appropriate auxiliary functions and technically using maximum principles, we establish conditions to guarantee that the solution blows up in some finite time or remains global. In addition, the upper estimates of blow-up rate and global solution are specified. We also obtain an upper bound of blow-up t...