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Liapunov functions and boundedness and global existence of solutions
Applicable Analysis, 1972In this paper the properties of a Liapunov function and its derivatives are combined in obtaining sufficient conditions for the boundedness and global existence of solutions of the system of differential equations x=f(t,x) (1) where f: [0,∞)XRn→ Rn is continuous.
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Global boundedness of solutions of anisotropic variational problems
1991The global boundedness of minimizers is proved for functionals \(\int_ \Omega f(x,Du)dx\) (\(\Omega\) bounded open subset of \(R^ n\)), where \(f(x,z)\) is a Carathéodory function, defined for \(x\in \Omega\), \(z\in R^ n\), satisfying anisotropic growth conditions: \[ f(x,z)\geq m\sum^ n_{i=1}|\xi_ i|^{q_ i} (m>0, q_ i>1),\quad f(x,0)\in L^ r(\Omega ...
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Global Existence and Boundedness of Solutions to the Extensible Beam Equation
SIAM Journal on Mathematical Analysis, 1982The theory of semigroups of linear operators and the recently developed theory of cosine operators is used to provide a variation of parameters representation of solutions to the equation governing the transverse motion of an extensible beam and to insure $L^2 $ boundedness of these solutions.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Global patterns in excess body weight and the associated cancer burden
Ca-A Cancer Journal for Clinicians, 2019Hyuna Sung +2 more
exaly