?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Facta.bibl.u-szeged.hu%2F56904%2F&rft.title=Nonoscillatory+solutions+of+planar+half-linear+differential+systems%3A+a+Riccati+equation+approach&rft.creator=+Jaro%C5%A1+Jaroslav&rft.creator=+Takasi+Kusano&rft.creator=+Tanigawa+Tomoyuki&rft.description=In+this+paper+an+attempt+is+made+to+depict+a+clear+picture+of+the+overall+structure+of+nonoscillatory+solutions+of+the+first+order+half-linear+differential+system+x+0+%E2%88%92+p(t)%CF%951%2F%CE%B1+(y)+%3D+0%2C+y+0+%2B+q(t)%CF%95%CE%B1(x)+%3D+0%2C+(A)+where+%CE%B1+%3E+0+is+a+constant%2C+p(t)+and+q(t)+are+positive+continuous+functions+on+%5B0%2C+%E2%88%9E)%2C+and+%CF%95%CE%B3(u)+%3D+%7Cu%7C+sgn+u%2C+u+%E2%88%88+R%2C+%CE%B3+%3E+0.+A+systematic+analysis+of+the+existence+and+asymptotic+behavior+of+solutions+of+(A)+is+proposed+for+this+purpose.+A+special+mention+should+be+made+of+the+fact+that+all+possible+types+of+nonoscillatory+solutions+of+(A)+can+be+constructed+by+solving+the+Riccati+type+differential+equations+associated+with+(A).+Worthy+of+attention+is+that+all+the+results+for+(A)+can+be+applied+to+the+second+order+half-linear+differential+equation+(p(t)%CF%95%CE%B1(x+0+))0+%2B+q(t)%CF%95%CE%B1(x)+%3D+0%2C+(E)+to+build+automatically+a+nonoscillation+theory+for+(E).&rft.date=2018&rft.type=Foly%C3%B3irat&rft.type=NonPeerReviewed&rft.format=part&rft.language=hu&rft.identifier=http%3A%2F%2Facta.bibl.u-szeged.hu%2F56904%2F1%2Fejqtde_2018_092.pdf&rft.identifier=+++Jaro%C5%A1+Jaroslav%3B++Takasi+Kusano%3B++Tanigawa+Tomoyuki%3A+++Nonoscillatory+solutions+of+planar+half-linear+differential+systems%3A+a+Riccati+equation+approach.++(2018)+++