Nonlinear Functional Analysis and Its Applications: I: Fixed-Point TheoremsSpringer, 13 dic 1985 - 909 páginas The greatest mathematicians, such as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. Felix Klein There exists the remarkable possibility that one can master a subject mathemati cally, without really understanding its essence. Albert Einstein Don't give us numbers: give us insight! A contemporary natural scientist to a mathematician Numerous questions in physics, chemistry, biology, and economics lead to nonlinear problems; for example, deformation of rods, plates, and shells; behavior of plastic materials; surface waves of fluids; flows around objects in fluids or gases; shock waves in gases; movement of viscous fluids; equilibrium forms of rotating fluids in astrophysics; determination of the shape of the earth through gravitational measu- ments; behavior of magnetic fields of astrophysical objects; melting processes; chemical reactions; heat radiation; processes in nuclear reactors; nonlinear oscillation in physics, chemistry, and biology; 2 Introduction existence and stability of periodic and quasiperiodic orbits in celestial mechanics; stability of physical, chemical, biological, ecological, and economic processes; diffusion processes in physics, chemistry, and biology; processes with entropy production, and self-organization of systems in physics, chemistry, and biology; study of the electrical potential variation in the heart through measure ments on the body surface to prevent heart attacks; determining material constants or material laws (e. g. |
Índice
Introduction | 1 |
CHAPTER | 16 |
APPLICATIONS OF THE FUNDAMENTAL | 71 |
Página de créditos | |
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Otras ediciones - Ver todo
Nonlinear Functional Analysis and Its Applications: I: Fixed-Point Theorems Eberhard Zeidler Vista de fragmentos - 1985 |
Nonlinear Functional Analysis and its Applications: I: Fixed-Point Theorems Eberhard Zeidler No hay ninguna vista previa disponible - 1985 |
Nonlinear Functional Analysis and its Applications: I: Fixed-Point Theorems Eberhard Zeidler No hay ninguna vista previa disponible - 2011 |
Términos y frases comunes
A₁ algebraic analytic applications asymptotically B-spaces Banach behavior bifurcation point bifurcation theory boundary boundary-value problem bounded branching equations Brouwer fixed-point theorem Chapter classical coefficients compact condition consider continuous convergence convex convex set Corollary definition denote differential equations eigenvalue equilibrium exactly one solution example exists F-derivative Figure finitely fixed point fixed-point index Fredholm operator h₁ Hint homeomorphism Hopf bifurcation implicit function theorem implies important integral equations iterative method Let f linear operator Lipschitz continuous main theorem manifolds map F mapping degree mathematical maximum principle monotone increasing multivalued map neighborhood Newton's method nonempty nonlinear obtain open set operator equation order cone oscillations parameter perturbation positive priori estimates Prob PROOF Prop Proposition regular respect satisfied Section sequence solve space spectral radius stability supersolution Suppose topological uniqueness x₁ Xn+1 zero