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Applicable Analysis
An International Journal
Volume 1, 1971 - Issue 1
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Original Articles

On the solutions of certain linear nonhomogeneous second-order differential equations

Marvin S. Keener Oklahoma State University, Stillwater, Oklahoma
Pages 57-63 | Published online: 04 Mar 2011

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Wan-Tong Li & Ravi P. Agarwal. (2000) Interval oscillation criteria for a forced second order nonlinear ordinary differential equation. Applicable Analysis 75:3-4, pages 341-347.
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N. PARHI, S. K. Nayak & W Leighton. (1979) On the Behaviour of Solutions of . Applicable Analysis 9:1, pages 1-5.
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Lu-San Chen & Cheh-Chih Yeh. (1979) On the comparison theorem for non-homogeneous second order differential inequalities. Applicable Analysis 8:4, pages 195-199.
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G.A. Grigorian. (2022) Oscillation and non-oscillation criteria for linear nonhomogeneous systems of two first-order ordinary differential equations. Journal of Mathematical Analysis and Applications 507:1, pages 125734.
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Abdullah ?zbekler. (2017) Sturmian comparison theory for half-linear and nonlinear differential equations via Picone identity. Mathematical Methods in the Applied Sciences 40:8, pages 3100-3110.
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Haidong Liu & Fanwei Meng. (2016) Interval oscillation criteria for second-order nonlinear forced differential equations involving variable exponent. Advances in Difference Equations 2016:1.
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A. ?zbekler. (2015) Sturmian theory for second order differential equations with mixed nonlinearities. Applied Mathematics and Computation 259, pages 379-389.
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Seshadev Padhi & Smita PatiSeshadev Padhi & Smita Pati. 2014. Theory of Third-Order Differential Equations. Theory of Third-Order Differential Equations 147 191 .
Seshadev Padhi & Smita PatiSeshadev Padhi & Smita Pati. 2014. Theory of Third-Order Differential Equations. Theory of Third-Order Differential Equations 1 44 .
A. Özbekler & A. Zafer. 2013. Differential and Difference Equations with Applications. Differential and Difference Equations with Applications 183 195 .
Taher S. Hassan & Qingkai Kong. (2012) INTERVAL CRITERIA FOR FORCED OSCILLATION OF DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN AND NONLINEARITIES GIVEN BY RIEMANN-STIELTJES INTEGRALS. Journal of the Korean Mathematical Society 49:5, pages 1017-1030.
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Fanwei Meng & Yan Huang. (2011) Interval oscillation criteria for a forced second-order nonlinear differential equations with damping. Applied Mathematics and Computation 218:5, pages 1857-1861.
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A. ?zbekler, J.S.W. Wong & A. Zafer. (2011) Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients. Applied Mathematics Letters 24:7, pages 1225-1230.
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Taher S. Hassan, Lynn Erbe & Allan Peterson. (2011) Forced oscillation of second order differential equations with mixed nonlinearities. Acta Mathematica Scientia 31:2, pages 613-626.
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A. ?zbekler & A. Zafer. (2010) Principal and nonprincipal solutions of impulsive differential equations with applications. Applied Mathematics and Computation 216:4, pages 1158-1168.
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Jing Shao & Fanwei Meng. (2010) Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed Argument. International Journal of Differential Equations 2010, pages 1-15.
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A. Nandakumaran & S. Panigrahi. (2009) Oscillation criteria for differential equations of second order. Mathematica Slovaca 59:4, pages 433-454.
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Chenshun Li & Shuming Chen. (2009) Oscillation of second-order functional differential equations with mixed nonlinearities and oscillatory potentials. Applied Mathematics and Computation 210:2, pages 504-507.
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Yan Huang & Fanwei Meng. (2009) Oscillation criteria for forced second-order nonlinear differential equations with damping. Journal of Computational and Applied Mathematics 224:1, pages 339-345.
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Yuan Gong Sun & Fan Wei Meng. (2008) Interval criteria for oscillation of second-order differential equations with mixed nonlinearities. Applied Mathematics and Computation 198:1, pages 375-381.
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Yuan Gong Sun & James S.W. Wong. (2007) Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities. Journal of Mathematical Analysis and Applications 334:1, pages 549-560.
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Wenying Shi. (2006) Interval oscillation criteria for a forced second-order differential equation with nonlinear damping. Mathematical and Computer Modelling 43:1-2, pages 170-177.
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D. ?akmak & A. Tiryaki. (2005) Oscillation criteria for certain forced second-order nonlinear differential equations with delayed argument. Computers & Mathematics with Applications 49:11-12, pages 1647-1653.
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Yuan Gong Sun, C.H. Ou & J.S.W. Wong. (2004) Interval oscillation theorems for asecond-order linear differential equation. Computers & Mathematics with Applications 48:10-11, pages 1693-1699.
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Yuan Gong Sun & James S.W. Wong. (2004) Note on forced oscillation of nth-order sublinear differential equations. Journal of Mathematical Analysis and Applications 298:1, pages 114-119.
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Wan-Tong Li. (2004) Interval oscillation criteria for second-order quasi-linear nonhomogeneous differential equations with damping. Applied Mathematics and Computation 147:3, pages 753-763.
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Yuan Gong Sun. (2003) A note on Nasr's and Wong's papers. Journal of Mathematical Analysis and Applications 286:1, pages 363-367.
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James S.W. Wong. (1999) Oscillation Criteria for a Forced Second-Order Linear Differential Equation. Journal of Mathematical Analysis and Applications 231:1, pages 235-240.
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A.A.S. Zaghrout & A.A. Ragab. (1990) OSCILLATORY BEHAVIOUR OF SOLUTIONS OF . Acta Mathematica Scientia 10:3, pages 355-360.
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James S. W. Wong. (1988) Second Order Nonlinear Forced Oscillations. SIAM Journal on Mathematical Analysis 19:3, pages 667-675.
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Xunming Liu & Qingyi Chen. (1986) OSCILLATORY FUNCTIONS AND SECOND ORDER LINEAR EQUATIONS. Acta Mathematica Scientia 6:4, pages 445-452.
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N. Parhi & S.K. Nayak. (1984) Nonoscillation of second-order nonhomogeneous differential equations. Journal of Mathematical Analysis and Applications 102:1, pages 62-74.
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M. S. Keener & C. C. Travis. (1980) Sturmian theory for a class of nonselfadjoint differential systems. Annali di Matematica Pura ed Applicata 123:1, pages 247-266.
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Paul W. Spikes & Wanda W. Smith. (1980) Some asymptotic properties of the solutions of perturbed nonlinear differential equations. Annali di Matematica Pura ed Applicata 125:1, pages 117-133.
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F. V. Atkinson, R. C. Grimmer & W. T. Patula. (1980) Nonoscillatory solutions of forced second order linear equations. - II. Annali di Matematica Pura ed Applicata 126:1, pages 299-317.
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John R. Graef. (1979) A comparison and oscillation result for second order nonlinear differential equations. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 49:1, pages 74-76.
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H. C. Howard. (1978) Oscillation and nonoscillation criteria for nonhomogeneous differential equations. Annali di Matematica Pura ed Applicata 118:1, pages 163-180.
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John R. Graef & Paul W. Spikes. (1978) Comparison and nonoscillation results for perturbed nonlinear differential equations. Annali di Matematica Pura ed Applicata (1923 -) 116:1, pages 135-142.
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John R. Graef. (1977) Oscillation, nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order. Journal of Mathematical Analysis and Applications 60:2, pages 398-409.
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R.E Sitter & S.C Tefteller. (1977) Oscillation of a fourth-order nonhomogeneous differential equation. Journal of Mathematical Analysis and Applications 59:1, pages 93-104.
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Thomas Wallgren. (1976) Oscillation of Solutions of the Differential Equation $y'' + p(x)y = f(x)$. SIAM Journal on Mathematical Analysis 7:6, pages 848-857.
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S. C. Tefteller. (1976) Oscillation of Second Order Nonhomogeneous Linear Differential Equations. SIAM Journal on Applied Mathematics 31:3, pages 461-467.
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Samuel M. RankinIIIIII. (1976) Oscillation theorems for second-order nonhomogeneous linear differential equations. Journal of Mathematical Analysis and Applications 53:3, pages 550-553.
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Samuel M. Rankin. (1976) Oscillation of a forced second order nonlinear differential equation. Proceedings of the American Mathematical Society 59:2, pages 279-282.
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JOHN R. GRAEF & PAUL W. SPIKES. 1976. Dynamical Systems. Dynamical Systems 275 278 .
Kent Foster. (1976) Criteria for oscillation and growth of nonoscillatory solutions of forced differential equations of even order. Journal of Differential Equations 20:1, pages 115-132.
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Shoshana Abramovich. (1975) On the behavior of the solutions of y? + p(x)y = ?(x). Journal of Mathematical Analysis and Applications 52:3, pages 465-470.
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Alexandra Skidmore & John J Bowers. (1975) Oscillatory behavior of solutions of y? + p(x)y = f(x). Journal of Mathematical Analysis and Applications 49:2, pages 317-323.
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R.S. Dahiya & Bhagat Singh. (1974) On the oscillation of a second-order delay equation. Journal of Mathematical Analysis and Applications 48:2, pages 610-617.
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Bhagat Singh & R.S. Dahiya. (2009) Nonoscillation of third order retarded equations. Bulletin of the Australian Mathematical Society 10:1, pages 9-14.
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Alexandra Skidmore & Walter Leighton. (1973) On the differential equation y? + p(x)y = f(x). Journal of Mathematical Analysis and Applications 43:1, pages 46-55.
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Bhagat Singh. (1973) Oscillation and nonoscillation of even-order nonlinear delay-differential equations. Quarterly of Applied Mathematics 31:3, pages 343-349.
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