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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.

Mountain pass theorem. --- Critical point theory (Mathematical analysis) --- Hamiltonian systems. --- Variational principles. --- Variational inequalities (Mathematics) --- Maxima and minima. --- Nonsmooth optimization. --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Minima --- Mathematics --- Extremum principles --- Minimal principles --- Variation principles --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Differential topology --- Global analysis (Mathematics) --- MPT (Mathematical analysis) --- Mountain pass theorem --- Hamiltonian systems --- Variational principles --- Variational inequalities --- Maxima and minima --- Nonsmooth optimization

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This Special Issue is a collection of high-quality reviews and original papers from editorial board members, guest editors, and leading researchers discussing new knowledge or new cutting-edge developments in the field of engineering.

hydrofoil optimization --- NSGA-II --- CFD --- XFOIL --- NACA 63815 --- bezier curve --- ultrasound application --- glass bottles --- fruit juice --- foam drainage --- foaming behavior --- martensitic phase transformation (MPT) --- grain misorientation (GMO) --- surface roughening (Ra) --- grain size (Dg) --- solid oxide fuel cell --- computational fluid dynamics --- sensitivity analysis --- optimization --- sand retention test --- sand control devices --- sand production --- sand replication --- SAGD --- probabilistic risk assessment --- multi-hazards --- nuclear safety --- dry-cured ham --- food-grade chemical --- coating --- mechanical performance characteristics --- chemical treatment --- ham nets --- pest management --- mechanical test --- mesh fabric --- artificial magnetic conductor (AMC) --- specific absorption rate (SAR) --- coplanar waveguide (CPW) antenna --- magneto-dielectric (MD) --- mobile phones --- wireless communications --- optical multi-band systems --- physical layer modeling --- fiber-optic communications --- commercially available components --- planar transformer --- eco-design --- environmental impact evaluation --- product efficiency --- DC-DC converter --- dual active bridge (DAB) --- life cycle optimization --- fuel optimization --- low cost HEV --- optimum hybridization --- bubble nucleation --- gas-liquid systems --- supersaturation --- step-down pressure --- Fick’s second law diffusion --- characteristic time --- Q factor --- damping model --- transitional flow regime --- viscous flow regime --- MEMS oscillator --- bending modes --- zirconium phosphate --- titanium phosphate --- nanolayered phosphates --- nanofibrous titanium phosphate --- chemical synthesis --- crystal structure --- technological applications --- drug delivery --- biomedical applications --- n/a --- Fick's second law diffusion