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Course Information
Philip Korman
Professor
806D Old Chemistry Building
513-556-4089
philip.korman@uc.edu
http://math.uc.edu/~kormanp/
Education
Ph.D., New York University, 1981.
Peer Reviewed Publications
Galstyan, A., & Li, Y. (2006). On the oscillations of the solution curve for a class of semilinear equations. J. Math. Anal. Applic., 321, 576-588.
(2006). Uniqueness and exact multiplicity of solutions of non-autonomous Dirichlet problems. Advanced Nonlinear Studies, 6, 461-481.
Ouyang, T. (2006). Positivity for the linearized problem for semilinear equations. Topol. Methods Nonlinear Anal., 28(1), 53-60.
Li, Yi, & Ouyang, T. (2005). Computing the location and the direction of bifurcation. Mathematical Research Letters, 12(5 & 6), 933-944.
(2005). On a principle of predatory exclusion. Applicable Analysis, 84(7), 707-712.
Shi, J. (2005). On Lane-Emden type systems. Discrete Contin. Dyn. Syst. 510-517.
(2004). Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems. Proc. Roy. Soc. Edinburgh Sect. A, 134(1), 179-190.
(2003). An accurate computation of the global solution curve for the Gelfandproblem through a two point approximation. Appl.Math and Computations, 139(2 & 3), 363-369.
(2003). Curves of positive solutions for supercritical problems. Applicable Analysis, 82, 45-54.
Li, Y., & Ouyang, T. (2003). Perturbation of global solution curves for semilinear problems. Adv. Nonlinear Stud., 3(2), 289-299.
(2002). On uniqueness of positive solutions for a class of semilinear problems. Discrete Contin. Dynam. Systems, 8(4), 865-871.
(2002). Curves of sign-changing solutions for semilinear equations. Nonlinear Analysis TMA, 51(5), 801-820.
(2002). Exact multiplicity of solutions for a class of Neumann problems. Comm. Appl. Nonlinear Anal., 9(4), 1-17.
(2002). Global solution curves for semilinear systems. Math. Methods Appl. Sci, 25(1), 3-20.
(2002). A remark on the non-degeneracy condition. Results in Mathematics, 41(3 & 4), 334–336.
(2002). Stability and Morse indices of solutions for two classes of semilinear problems. Comm. Appl. Nonlinear Anal., 9(4), 1-17.
(2001). Monotone approximations of unstable solutions. J. Comput. Appl. Math., 136, 309-315.
(2001). On multiplicity of solutions of semilinear equations. Mathematische Nachrichten, 229, 119-127.
Shi, J. (2001). New exact multiplicity results with an application to a population model. Proc. Royal Soc. Edinburgh Ser. A., 131(5), 1167-1182.
Shi, J. (2000). Instability and exact multiplicity of solutions of semilinear equations. Proceedings of the Conference on Nonlinear Differential Equations 311-322.
Li, Y. (2000). Infinitely many solutions at a resonance. Electron. J. Differ. Equ. Conf., 5.
(1999). Multiplicity of positive solutions for semilinear equations on circulardomains. Comm. Appl. Nonlinear Anal., 6(3), 17-35.
Li, Y. (1999). The exactness of S-shaped bifurcation curve. Proc. Amer. Math. Soc., 127, 1011-1020.
Li, Y. (1999). Generalized averages for solutions of two-point Dirichlet problems. J. Math. Anal. Appl., 239(2), 478-484.
Ouyang, T. (1999). Multiplicity and Morse indices of sign-changing solutions for semilinear equations. Canad. Appl. Math. Quart., 7(3), 239-250.
(1999). Exact multiplicity of positive solutions for a class of semilinear equations on a ball. Electron. J. Qual. Theory Differ. Equ., 8.
(1998). Remarks on Nagumo’s condition. Portugaliae Mathematica, 55(1), 1-9.
(1998). The global solution set for a class of semilinear problems. J. Math. Anal. Appl., 226, 101-120.
(1998). A global solution curve for a class of semilinear equations. Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations 119–127.
(1998). Uniqueness and exact multiplicity results for two classes of semilinear problems. Nonlinear Analysis TMA, 31, 849-865.
Li, Y., & Ouyang, T. (1997). An exact multiplicity result for a class of semilinear equations. Commun. in PDE, 22, 661-684.
(1997). Solution curves for semilinear equations on a ball. Proc. of Amer. Math. Soc., 125, 1997-2005.
(1997). Steady states and long time behavior of some convective reaction-diffusion equations. Funkcialaj Ekvacioj, 40, 165-183.
Lazer, A.C., & Li, Y. (1997). On homoclinic and heteroclinic orbits for Hamiltonian systems. Differential and Integral Equations, 10, 357-368.
Ouyang, T. (1996). Solution curves for two classes of boundary-value problems. Nonlinear Analysis Apllic., 27, 1031-1047.
Li, Y., & Ouyang, T. (1996). Exact multiplicity results for boundary value problems with nonlinearities generalizing cubic. Proc. Royal Soc. Edinburgh Ser. A., 126A, 599-616.
Ouyang, T. (1995). Exact multiplicity results for a class of boundary value problems with cubic nonlinearities. J. Math. Anal. Applic., 194, 328-341.
Ouyang, T. (1995). On computation of solution curves for semilinear elliptic problems. Numer. Funct. Anal. and Optimiz., 16(1 & 2), 219-231.
(1995). Symmetry of positive solutions for elliptic problems in one dimension. Applicable Analysis, 58, 351-365.
Ouyang, T. (1995). Exact multiplicity results for two classes of periodic. J. Math. Anal. Applic., 194, 763-779.
Ouyang, T. (1995). Multiplicity results for two classes of boundary-value problems. SIAM J. of Math. Analysis, 26(1), 180-189.
(1994). On the dynamics of two classes of periodic ecological models. J. of Computational and Appl. Math., 52, 267-275.
Lazer, A.C. (1994). Homoclinic orbits for a class of symmetric Hamiltonian systems. EJDE Volumes.
Ouyang, T. (1993). Exact multiplicity results for two classes of boundary value problems. Diff. and Integral Equations, 6(6), 1507-1517.
(1993). An Algorithmfor Computing Unstable Solutions of Semilinear Boundary Value Problems. Computing, 51(3 & 4), 327-334.
(1992). A Computer Assisted Study of Periodic Parabolic Problems. Appl. Math. & Computation, 50(2 & 3), 203-221.
(1992). Dynamics of the Lotka-Volterra Systems with Diffusion. Applicable Analysis, 44(3 & 4), 191-208.
Choudury, G. (1992). On Computation of Solutions of Fully Nonlinear Elliptic Problems. J. of Computational and Appl. Math, 41, 301-311.
(1992). On Periodic Solutions of Singular Perturbation Problems. Proceedings of the Royal Society of Edinburgh, 120A, 143-152.
(1992). Some New Results on the Periodic Competition Model. J. Math. Anal. Applic., 171(1), 131-138.
Barbu, V. (1991). Approximating Optimal Controls of Elliptic Obstacle Problem by Monotone Iteration Schemes. Numer. Funct. Anal. and Optimiz., 12(5 & 6), 429-442.
Choudury, G. (1991). On Computation of Solutions of Nonlinear Boundary Value Problems. Comput. Math. Appl., 22(8), 49-55.
Leung, A., & Stojanovic, S. (1990). Monotone Iterations for NonlinearObstacle Problems. J. Austr. Math. Soc. Ser., B 30, 259-276.
(1990). On Existence of Periodic Solutions for a Class of Quasilinear Non-Coercive Problems. Funkcialaj Ekvacioj, 33, 127-138.
(1990). On Periodic Solutions for Singular Perturbation Problems. Nonlinear Analysis TMA, 15(5), 467-478.
(1989). On Computation of Solutions of Elliptic Systems. Numer. Funct. Anal. and Optimiz., 10(9 & 10), 977-990.
(1989). On Existence of Solutions for a Class of Fully Nonlinear Noncoercive Problems. J. Math. Anal. Applic., 137, 477-484.
(1989). On Existence of Solutions for a Class of Non-Coercive Problems. Commun. in PDE, 14(4), 519-539.
(1989). A MaximumPrinciple for Fourth Order Ordinary Differential Equations. Applicable Analysis, 33, 267-273.
(1988). On Blow-Up of Solutions of Nonlinear Evolution Equations. Proc. Amer. Math. Soc., 103, 189-197.
(1988). Computation of Displacements for Nonlinear Elastic Beam Models Using Monotone Iterations. Intern. J. Math. and Math. Sci., 11, 121-128.
(1988). On Existence of Solutions for Several Classes of Free Boundary Problems. SIAM J. Math. Anal., 19, 814-823.
(1987). On the Existence and Uniqueness of Positive Steady States in the Volterra-Lotka Ecological Models with Diffusion. Applicable Analysis, 26, 145-160.
Leung, A. (1986). A General Monotone Scheme for Elliptic Systems withApplications to Ecological Models. Proc. Royal Soc. Edinburgh, 102A, 315-325.
(1986). Existence and Approximation of Solutions of Inverse-Positive Problems. Nonlinear Analysis TMA, 10, 863-872.
(1986). Existence of Solutions for a Class of Semilinear Noncoercive Problems. Nonlinear Analysis TMA, 10, 1471-1476.
(1984). On Application of Monotone Iteration Scheme to Nonlinear Non-Coercive Problems. Nonlinear Analysis TMA, 8, 97-105.
(1983). Existence of Periodic Solutions for a Class of Nonlinear Problems. Non-linear Analysis TMA, 7, 873-879.
(1983). Existence of Solutions for a Class of Nonlinear Non-Coercive Problems. Comm. Partial Diff. Eqs., 8, 819-846.
Book Chapters
(2006). Handbook of Differential Equations, Ordinary Differential Equations. In A. Canada, P. Drabek and A. Fonda (Eds.), Global solution branches and exact multiplicity of solutions for two point boundary value problems (pp. 547-606). North Holland: Elsevier Science.
Other Publications
(2002). The global solution set for a class of semilinear problems. Pure and Appl. Math., 225. New York: Dekker.
(2001). Similarity of solution branches for two-point semilinear problems. Proceedings of the Fifth Mississippi State Conference on Differential Equations and Computational Simulations. Mississippi State.
