Nonlinear boundary conditions Blow-up Boundary value problems Eigenvalues Eigenvalues and eigenfunctions Mathematical models Nonlinear eigenvalues P-Laplacian Problem solving Sobolev trace embedding Elliptic systems P-Laplace operator Parabolic equations Theorem proving Variational methods Variational problems Asymptotic behavior Bessel functions Boundary conditions Concentration-compactness principle Eigenvalue bounds Elliptic system Lattice points Minimization problems Non-linear boundary conditions Optimization P-Laplace Semi-discretization in space p-Laplacian p-laplace equations