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During the last three decades, the study of nonlinear analysis has been pursued vigorously and such activity has had great influence on other areas of science, as much as on mathematics. At the same time, convex analysis has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. These two mathematical disciplines have no borders and benefit each other. Now, there is a demand for new ideas and human technology based on reliable theoretical methodology. It is believed that international experts on nonlinear analysis and convex analysis can provide reasonable and optimal solutions to such problems if they cooperate with one another. This book constitutes the proceedings of a conference which had several unique features, and which was very important for the development of mathematical science and related areas all over the world.
Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.