Theodore W Laetsch

Interests

Research

Nonlinear functional analysis

Teaching

All entry level courses to all lower level grad courses, with statistics excepted.

Courses

Scholarly Contributions

Journals/Publications

• Laetsch, T. (1985). The theory of forced, convex, autonomous, two point boundary value problems. Rocky Mountain Journal of Mathematics, 15(1), 133-154.
• Laetsch, T. (1984). Minimax principles for convex eigenvalue problems. Journal of Mathematical Analysis and Applications, 102(2), 328-347.
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  Abstract: Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by σ* the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. σ* is characterized as the saddle value of a functional JA determined by A and defined on the Cartesian product of K and its dual K*. © 1984.
• Amann, H., & Laetsch, T. (1976). POSITIVE SOLUTIONS OF CONVEX NONLINEAR EIGENVALUE PROBLEMS.. Indiana University Mathematics Journal, 25(3), 259-270.
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  Abstract: Nonlinear elliptic eigenvalue problems are studied of the form Lx equals lambda F(x) in OMEGA , Bx equals O on the boundary of OMEGA . The lambda -set is determined for which the boundary value problem has at least two positive solutions.
• Laetsch, T. (1975). A uniqueness theorem for elliptic quasi-variational inequalities. Journal of Functional Analysis, 18(3), 286-287.
• Laetsch, T. (1975). CRITICAL SOLUTIONS OF AUTONOMOUS NONLINEAR BOUNDARY VALUE PROBLEMS.. Indiana University Mathematics Journal, 24(7), 651-658.
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  Abstract: The autonomous semilinear boundary value problem Lu equals lambda f(u) on (0, 1) is considered, where A (u; O) is identical to alpha u(O) minus alpha prime u prime (0) equals 0 and B(u; 1) is identical to beta u(1) plus beta prime u prime (1) equals 0.
• Laetsch, T. (1975). Nonlinear eigenvalue problems with monotonically compact operators. Aequationes Mathematicae, 12(1), 109-.
• Laetsch, T. (1975). Nonlinear eigenvalue problems with monotonically compact operators. Aequationes Mathematicae, 13(1-2), 61-76.
• Laetsch, T. (1975). Nonlinear eigenvalue problems with positively convex operators. Journal of Mathematical Analysis and Applications, 51(3), 653-669.
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  Abstract: We consider the equation u = λAu (λ > 0), where A is a forced isotone positively convex operator in a partially ordered normed space with a complete positive cone K. Let Λ be the set of positive λ for which the equation has a solution u ε{lunate} K, and let Λ0 be the set of positive λ for which a positive solution-necessarily the minimum one-can be obtained by an iteration un = λAun-1, u0 = 0. We show that if K is normal, and if Λ is nonempty, then Λ0 is nonempty, and each set Λ0, Λ is an interval with inf(Λ0) = inf(Λ) = 0 and sup(Λ0) = sup(Λ) (= λ*, say); but we may have λ* ∉ Λ0 and λ* ε{lunate} Λ. Furthermore, if A is bounded on the intersection of K with a neighborhood of 0, then Λ0 is nonempty. Let u0(λ) = limn→∞(λA)n(0) be the minimum positive fixed point corresponding to λ ε{lunate} Λ0. Then u0(λ) is a continuous isotone convex function of λ on Λ0. © 1975.
• Laetsch, T. (1974). Comparison and positivity theorems for linear and nonlinear boundary value problems. Journal d'Analyse Mathématique, 27(1), 24-46.
• Laetsch, T. (1973). Uniqueness for sublinear boundary value problems. Journal of Differential Equations, 13(1), 13-23.
• Laetsch, T. (1971). On the number of solutions of boundary value problems with convex nonlinearities. Journal of Mathematical Analysis and Applications, 35(2), 389-404.
• Cohen, D. S., & Laetsch, T. W. (1970). Nonlinear boundary value problems suggested by chemical reactor theory. Journal of Differential Equations, 7(2), 217-226.
• LAETSCH, T. (1970). EXISTENCE AND BOUNDS FOR MULTIPLE SOLUTIONS OF NONLINEAR EQUATIONS. SIAM Journal on Applied Mathematics, 18(2), 389-400.
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  Abstract: Author proves a general theorem which illustrates the method used to prove the existence of a solution, and points out that this theorem is applicable to a class of two-point boundary value problems and then shows how the results can be shaprened for a subclass of two- point boundary value problems for which the location of the maximum value of the solutions is known a priori. An example is given illustrating how the method may be applied to predict the existence of three solutions of a certain boundary value problem.