References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt155",{id:"formSmash:upper:j_idt155",widgetVar:"widget_formSmash_upper_j_idt155",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt157_j_idt159",{id:"formSmash:upper:j_idt157:j_idt159",widgetVar:"widget_formSmash_upper_j_idt157_j_idt159",target:"formSmash:upper:j_idt157:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Complex oscillations of non-definite sturm-liouville problemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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Number of Authors: 2
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, 314Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2016. 314
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:ltu:diva-61277ISI: 000390155500003OAI: oai:DiVA.org:ltu-61277DiVA: diva2:1060621
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt407",{id:"formSmash:j_idt407",widgetVar:"widget_formSmash_j_idt407",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt413",{id:"formSmash:j_idt413",widgetVar:"widget_formSmash_j_idt413",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt419",{id:"formSmash:j_idt419",widgetVar:"widget_formSmash_j_idt419",multiple:true});
##### Note

We expand upon the basic oscillation theory for general boundary problems of the form (Formula presented) where q and r are real-valued piecewise continuous functions and y is required to satisfy a pair of homogeneous separated boundary conditions at the end-points. The non-definite case is characterized by the indefiniteness of each of the quadratic forms (Formula presented) over a suitable space where B is a boundary term. In 1918 Richardson proved that, in the case of the Dirichlet problem, if r(t) changes its sign exactly once and the boundary problem is non-definite then the zeros of the real and imaginary parts of any non-real eigen-function interlace. We show that, unfortunately, this result is false in the case of two turning points, thus removing any hope for a general separation theorem for the zeros of the non-real eigen-functions. Furthermore, we show that when a non-real eigen-function vanishes inside I, the absolute value of the difference between the total number of zeros of its real and imaginary parts is exactly 2.

Validerad; 2017; Nivå 2; 2017-01-12 (andbra)

Available from: 2016-12-29 Created: 2016-12-29 Last updated: 2017-01-12Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1233",{id:"formSmash:lower:j_idt1233",widgetVar:"widget_formSmash_lower_j_idt1233",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1235_j_idt1245",{id:"formSmash:lower:j_idt1235:j_idt1245",widgetVar:"widget_formSmash_lower_j_idt1235_j_idt1245",target:"formSmash:lower:j_idt1235:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});