| Title |
Šturmo ir Liuvilio uždavinio su dvitaške nelokaliąja sąlyga spektro tyrimas / |
| Translation of Title |
Investigation of spectrum for a Sturm–Liouville problem with two-point nonlocal boundary conditions. |
| Authors |
Bingelė, Kristina |
| Full Text |
|
| Pages |
40 |
| Keywords [eng] |
Sturm–Liouville problem ; nonlocal two-point boundary condition ; spectrum curves ; characteristic function |
| Abstract [eng] |
In the thesis the spectrum of Sturm–Liouville Problem with one classical condition (Dirichlet or Neumann type boundary conditions) on the left side of the interval and another different type nonlocal two-point boundary condition or symmetrical type Nonlocal Condition on the right side of the interval is investigated. Characteristic Function is used to investigate the Spectrum Curves for such type of problems. We obtain general properties of the Characteristic Function and Spectrum Curves for such a problem. We get new results about complex eigenvalues. The properties of the Spectrum Curves for problems depend on Constant Eigenvalue Points and zeroes, poles, Critical Points of Characteristic Function. Investigations of real and complex parts of the spectrum are provided with the results of numerical experiments. The global view of Spectrum Domain depends on parameter ξ. At bifurcation points this view undergoes qualitative changes. We find bifurcation types for these Sturm–Liouville Problems. In the case of discrete Sturm–Liouville Problem a relation between eigenvalues and eigenvalue points is more complicated. For discrete Sturm–Liouville Problem we have two Ramification Points. The spectrum depends on discretization parameter. For discrete case we can investigate Spectrum Curves near infinity. This point is either Pole Point or Removable Singularity Point. We get new results about negative and large positive eigenvalues. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Summaries of doctoral thesis |
| Language |
Lithuanian |
| Publication date |
2019 |
