Dr. Alan V Lair
Professor

 

Contact:
Comm: 937-255-3636 x4519
DSN: 785-3636 x4519
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Education

Ph.D. (Mathematics) Texas Tech University, 1976

M.S. (Mathematics) Texas Tech University, 1972

B.A. (Mathematics) North Texas State University, 1970

Publications

Refereed Journal Articles:

1. J. R. Cannon, W. T. Ford and A. V. Lair, Quasilinear parabolic systems, Journal of Differential Equations 20 (1976), 441-472. MR 53 #1028.

2. A. V. Lair, A Rellich compactness theorem for sets of finite volume, American Mathematical Monthly 83 (1976), 350-351. MR 53 #6308.

3. A. V. Lair, A unique continuation theorem involving a degenerate parabolic operator, Proceedings of the American Mathematical Society 66 (1977), 41-45. MR 57 #6841.

4. A. V. Lair, Quasilinear elliptic systems, Annali di Matematica pura ed applicata CXVI (1978), 17-56. MR 81i:35073.

5. A. V. Lair, Uniqueness for a forward backward diffusion equation, Transactions of the American Mathematical Society 291 (1985), 311-317. MR 86j:35091.

6. A. V. Lair, Uniqueness for singular backward parabolic inequalities, Proceedings of the American Mathematical Society 98 (1986), 56-60. MR 87g:35107.

7. A. V. Lair, Uniqueness for a forward backward diffusion equation with smooth constitutive function, Applicable Analysis 29 (1988), 177-189. MR 90c:35114.

8. A. V. Lair, A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities, International Journal of Mathematics and Mathematical Sciences 13 (1990), 253-270. MR 91d:34013.

9. A. V. Lair, Uniqueness for a nonlinear abstract Cauchy problem, Pacific Journal of Mathematics 144 (1990), 105-129. MR 91f:34082.

10. A. V. Lair, The rate of spatial decay of nonnegative solutions of nonlinear parabolic equations and inequalities, Proceedings of the American Mathematical Society 112 (1991), 1077-1081. MR 91j:35157.

11. A. V. Lair, Uniqueness for the Cauchy problem for nonlinear parabolic equations and inequalities, Applicable Analysis 41 (1991), 221-236. MR 92d:35148.

12. A. V. Lair, Finite extinction time for solutions of nonlinear parabolic equations, Nonlinear Analysis 21 (1993), 1-8. MR 94e:35080.

13. A. V. Lair and M. E. Oxley, Extinction in finite time of solutions to nonlinear absorption-diffusion equations, Journal of Mathematical Analysis and Applications 182 (1994), 857-866. MR 95e:35093.

14. A. V. Lair and M. E. Oxley, Finite extinction time for a nonlinear parabolic Neumann boundary value problem, Applicable Analysis 55 (1994), 41-50. MR 96m:35174.

15. A. V. Lair and M. E. Oxley, Anisotropic nonlinear diffusion with absorption: existence and extinction, International Journal of Mathematics and Mathematical Sciences 19 (1996), 427-434. MR 97a:35099.

16. A. V. Lair and A. W. Shaker, Entire solution of a singular semilinear elliptic problem, Journal of Mathematical Analysis and Applications 200 (1996), 498-505. MR 97d:35063.

17. A. V. Lair and A. W. Shaker, Uniqueness of solution to a singular quasilinear elliptic problem, Nonlinear Analysis 28 (1997), 489-493. MR 98a:35039

18. A. V. Lair and A. W. Shaker, Classical and weak solutions of a singular semilinear elliptic problem, Journal of Mathematical Analysis and Applications 211 (1997), 371-385. MR 98d:35077

19. A. V. Lair and M. E. Oxley, A necessary and sufficient condition for global existence for a degenerate parabolic boundary value problem, Journal of Mathematical Analysis and Applications 221 (1998), 338-348. MR 99a:35143.

20. A. V. Lair and A. W. Wood, Large solutions of semilinear elliptic problems, Nonlinear Analysis 37 (1999), 805-812. MR 2000d:35075

21. A. V. Lair and A. W. Wood, Large solutions of semilinear elliptic equations with nonlinear gradient terms, International Journal of Mathematics and Mathematical Sciences 22 (1999), 869-883. MR 2000m:35074

22. A. V. Lair, A necessary and sufficient condition for existence of large solutions to semilinear elliptic equations, Journal of Mathematical Analysis and Applications 240 (1999), 205-218. MR 2000i:35046

23. A. V. Lair and A. W. Wood, Large solutions of sublinear elliptic equations, Nonlinear Analysis 39 (2000), 745-753. MR 2000m:35073

24. A. V. Lair and A. W. Wood, Existence of entire large positive solutions of semilinear elliptic systems, Journal of Differential Equations 164 (2000), 380-394. MR 2001j:35062

25. A. V. Lair, Nonradial large solutions of sublinear elliptic equations, Applicable Analysis 82 (2003), 431-437. MR 2004b:35102

26. A. V. Lair, A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system, International Journal of Mathematics and Mathematical Sciences 2005:11 (2005), 1809-1818. MR 2006e:35154.

27. A. V. Lair, Large solutions of semilinear elliptic equations under the Keller-Osserman condition, Journal of Mathematical Analysis and Applications 328 (2007), 1247-1254. MR 2007i:35077

28. A. V. Lair, Z. J. Proano, and A. W. Wood, Existence of large solutions to non-monotone semilinear elliptic equations, The Australian Journal of Mathematical Analysis and Applications 4, Issue 2, Article 14 (2007), 1-7.

29. A. V. Lair, Large solutions of mixed sublinear/superlinear elliptic equations, Journal of Mathematical Analysis and Applications 346 (2008), 99-106.

30. A. V. Lair and A. Mohammed, Entire large solutions of semilinear elliptic equations of mixed type, Communications on Pure and Applied Analysis8, No. 5 (2009), 1607-1618.

31. A. V. Lair, A necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems, Journal of Mathematical Analysis and Applications 365 (2010), 103-108.

32. A. V. Lair, Nonradial entire large solutions of semilinear elliptic equations, Journal of Partial Differential Equations 23, No. 4 (2010), 366-373.

33. A. V. Lair, Entire large solutions to semilinear elliptic systems, Journal of Mathematical Analysis and Applications 382 (2011), 324-333.

34. A. V. Lair and A. Mohammed, Entire large solutions to elliptic equations of power non-linearities with variable exponents, Advanced Nonlinear Studies 13 (2013), 699-719

35. A.V. Lair and A. Mohammed, Large solutions to semi-linear elliptic systems with variable exponents, Journal of Mathematical Analysis and Applications. 420, (2014), 1478-1499

 

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