π/4-tangentiality of solutions for one-dimensional Minkowski-curvature problems

Abstract

We analyze π4$\begin{array}{} \frac{\pi}{4} \end{array} $-tangentiality of solutions for several types of scalar equations and systems of one-dimensional Minkowski-curvature problems with two points Dirichlet boundary conditions, which is dependent on singularity of weight functions and the growth of nonlinear terms. One of the goals is to show non π4$\begin{array}{} \frac{\pi}{4} \end{array} $-tangentiality (∥u′∥∞ < 1) of solutions for some of the above problems. We consider a larger class of weight functions and find out suitable nonlinear terms associated with it to keep non π4$\begin{array}{} \frac{\pi}{4} \end{array} $-tangentiality of solutions. Finally, we obtain Lyapunov-type inequalities for some nonlinear problems as by-products which also extend the results in some previous studies.

Keywords

• minkowski-curvature
• singular weight
• π/4-tangentiality
• lyapunov-type inequality
• 34b16
• 34b60
• 34c40