Localization of critical points via mountain pass type theorems


REZUMAT: Metode itera\U{21b}iior monotone pentru problema cu valori ini\U{21b}iale relativ\u{a} la o ecua\U{21b}ie integral\u{a} din biomatematic\u{a}. \^{I}n lucrare este prezentat\u{a} o metod\u{a} constructiv\u{a} de rezolvare a problemei (1)-(2) \^{\i}n ipotezele (i)-(iv) presupun\^{a}nd c\u{a} func\U{21b}ia \(f(t,x))\ este monoton\u{a} \^{\i}n raport cu \(x)\.
Un aspect nou con\U{21b}inut \^{\i}n acest articol \^{\i}l constituie adaptarea metodei itera\U{21b}iilor monotone la cazul operatorilor anti-izotoni, \^{\i}n particular, la cazul c\^{a}nd \(f(t,x))\ este o func\U{21b}ie
necresc\u{a}toare \^{\i}n \(x)\.


REZUMAT: Metode iterative \U{21b}iior monotone pentru problema cu valori inițiale relative la o ecuație integrală din biomatematică. În lucrare este prezentată o metodă constructivă de rezolvare a problemei (1)-(2) și în ipotezele (i)-(iv) presupunând că funcția (f(t,x)) este monotonă și în raport cu (x). Un aspect nou conținut și în acest articol îl constituie adaptarea metodei iterațiilor monotone la cazul operatorilor anti-izotoni, și în particular, la cazul când (f(t,x)) este o funcție necrescătoare și în (x).


Radu Precup
Department of Mathematics, ”Babeș-Bolyai” University, Cluj-Napoca, Romania



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R. Precup, Localization of critical points via mountain pass type theorems, in Critical Point Theory and Its Applications, Proceedings of the International Summer School on Critical Point Theory and Applications Cluj-Napoca, July 9th-July 13th 2007, Cs. Varga, A. Kristaly and P.A. Blaga eds., Casa Cartii de Stiinta, Cluj-Napoca, 2007, 53-67.


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