"Oscillation theory of half-linear differential and difference equations"@en . "V navrhovan\u00E9m\u00A0projektu\u00A0budou studov\u00E1ny\u00A0kvalitativn\u00ED vlastnosti \u0159e\u0161en\u00ED pololine\u00E1rn\u00EDch diferenci\u00E1ln\u00EDch rovnic.\u00A0Je zn\u00E1mo, \u017Ee pololine\u00E1rn\u00ED rovnice m\u00E1 podobn\u00E9 vlastnosti jako Sturm-Liouvilleova line\u00E1rn\u00ED diferenci\u00E1ln\u00ED rovnice, kter\u00E1 je speci\u00E1ln\u00EDm p\u0159\u00EDpadem pololine\u00E1rn\u00ED rovnice. Hlavn\u00ED pozornost bude v\u011Bnov\u00E1na n\u00E1sleduj\u00EDc\u00EDm ot\u00E1zk\u00E1m:\u00A01. Odvozen\u00ED nov\u00FDch oscila\u010Dn\u00EDch a neoscila\u010Dn\u00EDch krit\u00E9ri\u00ED pro pololine\u00E1rn\u00ED rovnice varia\u010Dn\u00EDm principem a Riccatiho metodou.\u00A02. Nalezen\u00ED dal\u0161\u00EDch podm\u00EDnek charakterizuj\u00EDc\u00EDch hlavn\u00ED a nehlavn\u00ED \u0159e\u0161en\u00ED.\u00A03. Studium pololine\u00E1rn\u00ED diferen\u010Dn\u00ED rovnice, kter\u00E1 je\u00A0diskr\u00E9tn\u00ED analogi\u00ED diferenci\u00E1ln\u00ED rovnice. Charakterizace recesivn\u00EDho \u0159e\u0161en\u00ED diferen\u010Dn\u00ED rovnice."@cs . . "1"^^ . . . "0"^^ . . . "Oscila\u010Dn\u00ED teorie pololine\u00E1rn\u00EDch diferenci\u00E1ln\u00EDch a diferen\u010Dn\u00EDch rovnic"@cs . "1"^^ . . "half-linear equation; Riccati equation; principal solution; recessive solution; oscillatory equation"@en . "244"^^ . "0"^^ . "In the present project there will be studied qualitative properties of half-linear differential equations. It is known that there exists a similarity between theories of these equations and the Sturm-Liouville equation which is the special case of the half-linear equation. Especially, the following questions will be discussed:\u00A01. New oscillation and nonoscillation criteria for half-linear equations will be formulate. The variational principle and the Riccati technique will be used.\u00A02. New conditions which characterize the principal solution of the half-linear equation will be given. 3. The half-linear difference equation which is the discrete counterpart of the half-linear equation will be studied."@en . . . . "244"^^ . "2007-01-01+01:00"^^ . "2009-12-31+01:00"^^ . . "1"^^ .