Oscillation of second-order elliptic equations with damping terms

Xu, Zhiting

doi:10.1016/j.jmaa.2005.10.002

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…has been studied extensively, e.g., see [14][15][16][17][18][19][20][21][22][23][24][25]28,29] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Sun–Wong type theorems for second order damped elliptic equations

2009

Journal of Mathematical Analysis and Applications

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The oscillation criteria of Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] are extended to the forced second order damped elliptic differential equation with mixed nonlinearitiesWhen N = 1, our results include and improve those of Nasr [A.H. Nasr, Sufficient conditions for the forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for a forced second order superlinear differential equation, Wong [J.S.W. Wong, Oscillation criteria for a forced second order linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240] for a forced second order linear differential equation, Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] for a forced second order differential equation with mixed nonlinearities. When N 2, our results are more general, and improve the oscillation criteria of Zhuang [R.-K. Zhuang, Annual oscillation criteria for second order nonlinear elliptic differential equations, J. Comput. Anal. Math. 217 (2008) 268-276] for a forced second order undamped elliptic differential equation.

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“…has been studied extensively, e.g., see [14][15][16][17][18][19][20][21][22][23][24][25]28,29] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Sun–Wong type theorems for second order damped elliptic equations

2009

Journal of Mathematical Analysis and Applications

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“…(1) and conversion of this equation into an ordinary differential equation. This argument has been used very effectively by many authors in various situations, see [3,5,6,8,[13][14][15][16]18,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Ordinary differential equations in the oscillation theory of partial half-linear differential equation

Mařík

2008

Journal of Mathematical Analysis and Applications

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Let Ω = {x ∈ R N : r 0 |x| < 1} with N 2 and r 0 ∈ (0,1). We study a kind of geometric oscillatory and asymptotic behaviour near |x| = 1 of all radially symmetric solutions u = u(x) of the p-Laplace partial differential equation (P) : −div(|∇u| p−2 ∇u) = f (|x|)|u| p−2 u in Ω , u = 0 on |x| = 1 for p > 1. Necessary and sufficient conditions on the coefficient f (|x|) are given such that u(x) oscillates near |x| = 1 and the surface area of graph Γ(u) ⊆ R N+1 of u(x) is finite-rectifiable oscillations, and infinite-nonrectifiable oscillations. The L 1-integrability and L p-nonintegrability of |∇u| on Ω for p > 1 are also considered. Mathematics subject classification (2010): 26B15, 26B35, 34A26, 34C10, 34D05, 35B05, 35J25.8] M. PAŠI´CPAˇPAŠIPAŠI´ PAŠI´C, Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type, J. Math. Anal. Appl., 335 (2007), 724-738. [9] M. PAŠI´CPAˇPAŠIPAŠI´ PAŠI´C, Fractal oscillations for a class of second-order linear differential equations of Euler type, J. Math. Anal. Appl., 341 (2008), 211-223. [10] M. PAŠI´CPAˇPAŠIPAŠI´ PAŠI´C, Rectifiable and unrectifiable oscillations for a generalization of the Riemann-Weber version of Euler differential equations, Georgian Math. J., 15 (2008), 759-774. [11] M. PAŠI´CPAˇPAŠIPAŠI´ PAŠI´C AND S. TANAKA, Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order, J. Math. Anal. Appl., 381 (2011), 27-42. [12] M. PAŠI´CPAˇPAŠIPAŠI´ PAŠI´C AND S. TANAKA, Fractal oscillations of self-adjoint and damped linear differential equations of second-order,

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Oscillation criteria for second order forced elliptic differential equations with mixed nonlinearities

2008

Computers & Mathematics with Applications

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Oscillation of second-order elliptic equations with damping terms

Abstract: Some oscillation criteria are given for the second-order elliptic differential equation with damping termsThe results are extensions of modified Riccati technique and include earlier results of Noussair and Swanson, Xu, and Zhang et al.

Cited by 5 publications

References 9 publications

Sun–Wong type theorems for second order damped elliptic equations

Sun–Wong type theorems for second order damped elliptic equations

Ordinary differential equations in the oscillation theory of partial half-linear differential equation

Oscillation criteria for second order forced elliptic differential equations with mixed nonlinearities

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