Liouville properties

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Liouville Properties and Critical Value of Fully Nonlinear Elliptic Operators

We prove some Liouville properties for suband supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in OrnsteinUhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully n...

Further Higher Monotonicity Properties of Sturm{liouville Function

Suppose that the function q(t) in the diierential equation (1) y 00 + q(t)y = 0 is decreasing on (b;1) where b 0. We give conditions on q which ensure that (1) has a pair of solutions y 1 (t); y 2 (t) such that the n-th derivative (n 1) of the function p(t) = y 2 1 (t) + y 2 2 (t) has the sign (?1) n+1 for suuciently large t and that the higher diierences of a sequence related to the zeros of s...

some spectral properties of sturm-liouville problem with transmission conditions

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

Liouville numbers

In this work, we define the concept of Liouville numbers as well as the standard construction to obtain Liouville numbers and we prove their most important properties: irrationality and transcendence. This is historically interesting since Liouville numbers constructed in the standard way where the first numbers that were proven to be transcendental. The proof is very elementary and requires on...