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IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 1 Ver. IV (Jan. - Feb. 2017), PP 22-29
www.iosrjournals.org
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 21 | Page
Some Qualitative Approach for Bounded Solutions of Some
Nonlinear Diffusion Equations with Non-Autonomous
Coefficients: Oscillation Criteria
Tadie
Mathematics Institut , Universitetsparken 5 2100 Copenhagen, Denmark †
Abstract:
I. Introduction
1.1 Preliminaries
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 22 | Page
II. Models Problems And Main Resultys
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 23 | Page
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 24 | Page
III. Basic Picone-Type Formulae
IV. Equations Without Damping Terms
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 25 | Page
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 26 | Page
V. Equations With Damping Terms
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 27 | Page
VI. Some Applications
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 28 | Page
Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non..
DOI: 10.9790/5728-1301042229 www.iosrjournals.org 29 | Page
References
[1]. J.I.Diaz; Nonlinear Differential equations and Free Boundaries. London, Pitman,1985.
[2]. N.Kawano, WM. Ni and S. Yotsutani; A generalized Pohozaev identity and its application, J.Math. Soc. Japan Vol.42,No3,1990
pp.541-564.
[3]. Claus Dohman ; Pohozaev-Type Inequality for a Quasilinear Haraux-Weissler Equation , Funkcialaj Ekvacioj 39 (1996) 389-397.
[4]. Tadi´e; Comparison Results for Quasilinear Elliptic equations via Picone-type Identity: Part II: cases where he coefficient of the
principal part depends on he unknown function J. Nonlinear Anal., T.M.A.,vol. 71(2009)e601-e606 .
[5]. Tadi´e ; Oscillation criteria for damped Quasilinear second-order Elliptic Equations , Electronic J. of Differential Equations vol.
2011(2011), No.151, pp.1-11.
[6]. Tadi´e ; ON STRONG OSCILLATION CRITERIA FOR BOUNDED SOLUTIONS FOR SOME QUASILINEAR SECOND ORDER
ELLIPTIC EQUATIONS , Communications in Mathematical Analysis, volume 13, Number 2, pp. 15-26 (2012) ISSN 1938-9787
[7]. Tadi´e ; Oscllation Criteria for Some Emden-Fowler Type Half-linear Elliptic Equations, Int. Journal of Math. Analysis, Vol.8,
2014, No.24 1165-1168. ( HIKARI Ltd, WWW.m-hikari.com)
[8]. Tadi´e ; OSCILLATION CRITERIA FOR BOUNDED SOLUTIONS FOR SOME NONLINEAR DIFFUSION EQUATIONS VIA
PICONE-TYPE FORMULAE, Communications in Mathematical Analysis, volume 12, Number 2, pp. 1-10 (2012) ISSN 1938-9787
[9]. Tian Ma & Shouhong Wang; Bifurcation Theory and Applications. World Scientific Publ.Co (June 2005). London, Pitman,1985.
[10]. Ravi P. Agarwal, Said R.Grace and Donal O’Regan; Oscillation Theory for Second Order Linear , Half-linear, Superlinear and
Sublinear Dynamic Equations. Kluwer , 2000.
[11]. J. Jaros, T. Kusano , N. Yosida; Picone-type Inequalities for Nonlinear Elliptic Equations and their Applications J. of Inequal. &
Appl. (2001), vol. 6, 387-404 .
[12]. T. Kusano, J. Jaros, N. Yoshida; A Picone-type identity and Sturmian comparison and oscillation theorems for a class of half-linear
partial differential equations of second order, Nonlinear Analysis, Vol. 40 (2000), 381-395.
[13]. NorioYoshida ; Forced oscillation criteria for superlinear-sublinear elliptic equations via picone-type inequality , J. Math. Anal.
Appl. 363(2010), 711-717.

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Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non-Autonomous Coefficients: Oscillation Criteria

  • 1. IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 1 Ver. IV (Jan. - Feb. 2017), PP 22-29 www.iosrjournals.org DOI: 10.9790/5728-1301042229 www.iosrjournals.org 21 | Page Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non-Autonomous Coefficients: Oscillation Criteria Tadie Mathematics Institut , Universitetsparken 5 2100 Copenhagen, Denmark † Abstract: I. Introduction 1.1 Preliminaries
  • 2. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 22 | Page II. Models Problems And Main Resultys
  • 3. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 23 | Page
  • 4. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 24 | Page III. Basic Picone-Type Formulae IV. Equations Without Damping Terms
  • 5. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 25 | Page
  • 6. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 26 | Page V. Equations With Damping Terms
  • 7. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 27 | Page VI. Some Applications
  • 8. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 28 | Page
  • 9. Some Qualitative Approach for Bounded Solutions of Some Nonlinear Diffusion Equations with Non.. DOI: 10.9790/5728-1301042229 www.iosrjournals.org 29 | Page References [1]. J.I.Diaz; Nonlinear Differential equations and Free Boundaries. London, Pitman,1985. [2]. N.Kawano, WM. Ni and S. Yotsutani; A generalized Pohozaev identity and its application, J.Math. Soc. Japan Vol.42,No3,1990 pp.541-564. [3]. Claus Dohman ; Pohozaev-Type Inequality for a Quasilinear Haraux-Weissler Equation , Funkcialaj Ekvacioj 39 (1996) 389-397. [4]. Tadi´e; Comparison Results for Quasilinear Elliptic equations via Picone-type Identity: Part II: cases where he coefficient of the principal part depends on he unknown function J. Nonlinear Anal., T.M.A.,vol. 71(2009)e601-e606 . [5]. Tadi´e ; Oscillation criteria for damped Quasilinear second-order Elliptic Equations , Electronic J. of Differential Equations vol. 2011(2011), No.151, pp.1-11. [6]. Tadi´e ; ON STRONG OSCILLATION CRITERIA FOR BOUNDED SOLUTIONS FOR SOME QUASILINEAR SECOND ORDER ELLIPTIC EQUATIONS , Communications in Mathematical Analysis, volume 13, Number 2, pp. 15-26 (2012) ISSN 1938-9787 [7]. Tadi´e ; Oscllation Criteria for Some Emden-Fowler Type Half-linear Elliptic Equations, Int. Journal of Math. Analysis, Vol.8, 2014, No.24 1165-1168. ( HIKARI Ltd, WWW.m-hikari.com) [8]. Tadi´e ; OSCILLATION CRITERIA FOR BOUNDED SOLUTIONS FOR SOME NONLINEAR DIFFUSION EQUATIONS VIA PICONE-TYPE FORMULAE, Communications in Mathematical Analysis, volume 12, Number 2, pp. 1-10 (2012) ISSN 1938-9787 [9]. Tian Ma & Shouhong Wang; Bifurcation Theory and Applications. World Scientific Publ.Co (June 2005). London, Pitman,1985. [10]. Ravi P. Agarwal, Said R.Grace and Donal O’Regan; Oscillation Theory for Second Order Linear , Half-linear, Superlinear and Sublinear Dynamic Equations. Kluwer , 2000. [11]. J. Jaros, T. Kusano , N. Yosida; Picone-type Inequalities for Nonlinear Elliptic Equations and their Applications J. of Inequal. & Appl. (2001), vol. 6, 387-404 . [12]. T. Kusano, J. Jaros, N. Yoshida; A Picone-type identity and Sturmian comparison and oscillation theorems for a class of half-linear partial differential equations of second order, Nonlinear Analysis, Vol. 40 (2000), 381-395. [13]. NorioYoshida ; Forced oscillation criteria for superlinear-sublinear elliptic equations via picone-type inequality , J. Math. Anal. Appl. 363(2010), 711-717.