Modeling of the quasibrittle fracture of concrete at meso-scale: Effect of classes of aggregates on global and local behavior

This paper establishes such a uniqueness principle that under [Formula: see text] the fractional order differential inequality [Formula: see text] has the property that if [Formula: see text] then a non-negative weak solution to [Formula: see text] is unique, and if [Formula: see text] then the uniqueness of a non-negative weak solution to [Formula: see text] occurs when and only when [Formula: see text], thereby innovatively generalizing Gidas–Spruck’s result for [Formula: see text] in [Formula: see text] discovered in [B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525–598].

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Global and local behavior of positive solutions of nonlinear elliptic equations

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160340406 ◽

1981 ◽

Vol 34 (4) ◽

pp. 525-598 ◽

Cited By ~ 525

Author(s):

B. Gidas ◽

J. Spruck

Keyword(s):

Positive Solutions ◽

Elliptic Equations ◽

Nonlinear Elliptic Equations ◽

Local Behavior ◽

Nonlinear Elliptic ◽

Global And Local

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Experimental characterization of the global and local behavior of multi-dowel LVL-connections under complex loading

Materials and Structures ◽

10.1617/s11527-015-0657-8 ◽

2015 ◽

Vol 49 (6) ◽

pp. 2407-2424 ◽

Cited By ~ 2

Author(s):

Thomas K. Bader ◽

Michael Schweigler ◽

Georg Hochreiner ◽

Bertil Enquist ◽

Michael Dorn ◽

...

Keyword(s):

Complex Loading ◽

Local Behavior ◽

Experimental Characterization ◽

Global And Local

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Global and local behavior of zeros of nonpositive type

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.01.004 ◽

2014 ◽

Vol 414 (1) ◽

pp. 273-284 ◽

Cited By ~ 2

Author(s):

Henk de Snoo ◽

Henrik Winkler ◽

Michał Wojtylak

Keyword(s):

Local Behavior ◽

Global And Local

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Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − yn − b and yn+1 = xn − |yn| + 1 Where b ≥ 4

Mathematics ◽

10.3390/math9121390 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1390

Author(s):

Busakorn Aiewcharoen ◽

Ratinan Boonklurb ◽

Nanthiya Konglawan

Keyword(s):

Periodic Solution ◽

Equilibrium Point ◽

Difference Equations ◽

Piecewise Linear ◽

Global Behavior ◽

Local Behavior ◽

Linear Difference Equations ◽

All Solutions ◽

Prime Period ◽

Global And Local

The aim of this article is to study the system of piecewise linear difference equations xn+1=|xn|−yn−b and yn+1=xn−|yn|+1 where n≥0. A global behavior for b=4 shows that all solutions become the equilibrium point. For a large value of |x0| and |y0|, we can prove that (i) if b=5, then the solution becomes the equilibrium point and (ii) if b≥6, then the solution becomes the periodic solution of prime period 5.

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