Dr. Alan V. Lair, Professor of Mathematics
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. MR2428275
30. A. V. Lair and A. Mohammed, Entire large solutions of semilinear elliptic equations of mixed type, Communications on Pure and Applied Analysis 8, No. 5 (2009), 1607-1618. MR2505289
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. MR2585080
32. A. V. Lair, Nonradial entire large solutions of semilinear elliptic equations, Journal of Partial Differential Equations 23, No. 4 (2010), 366-373. MR2778817
33. A. V. Lair, Entire large solutions to semilinear elliptic systems, Journal of Mathematical Analysis and Applications 382 (2011), 324-333. MR2805516
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. MR3098817
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. MR3240090
36. A. V. Lair, Entire large solutions to semilinear elliptic systems of competitive type, Journal of Partial Differential Equations 32, No. 1 (2019), 52-65. MR3967871
37. A. V. Lair and A. Mohammed, Necessary and sufficient conditions for the existence of large solutions to semilinear elliptic equations with gradient terms, Journal of Differential Equations 374 (2023), 593-631. MR4626422
38. A. V. Lair, A note on entire large solutions to semilinear elliptic systems of competitive type, Nonlinear Analysis 261 (2025),