By Kenneth L. Cooke, Joseph Wiener (auth.), Stavros Busenberg, Mario Martelli (eds.)

The assembly explored present instructions of analysis in hold up differential equations and comparable dynamical platforms and celebrated the contributions of Kenneth Cooke to this box at the celebration of his sixty fifth birthday. the amount includes 3 survey papers reviewing 3 parts of present examine and seventeen study contributions. The learn articles take care of qualitative houses of options of hold up differential equations and with bifurcation difficulties for such equations and different dynamical platforms. A spouse quantity within the biomathematics sequence (LN in Biomathematics, Vol. 22) includes contributions on contemporary developments in inhabitants and mathematical biology.

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5 we deduce that there exists T > 0 such that if |y| > L then vp (x, y) ≥ 1 − 2δ for any x > T and vp (x, y) ≤ −1 + 2δ for any x < −T. 23) We will assume that T is such that also 1 − |z0 (x)| ≥ 2δ for any |x| ≥ T . Assume now by contradiction that vp (x, y) does not converge to ±1 as x → ±∞ uniformly with respect to y ∈ R. Then there exists a sequence (xj , yj ) ⊂ R2 such that |xj | → ∞, |yj | → ∞ as j → ∞ and 1 − |vp (xj , yj )| ≥ 2r > 0 for any j ∈ N. Since vp C 2 (R2 ) < +∞ we obtain that there exists ρ ∈ (0, 1) such that 1 − |vp (x, y)| ≥ r for any (x, y) ∈ ∪j∈N Bρ ((xj , yj )) (as usual we denote Bρ ((xj , yj )) = {(x, y) ∈ R2 / (x − xj )2 + (y − yj )2 < ρ2 }).

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Allen and J. W. , 27 (1979), 1085–1095. [6] L. Ambrosio and X. Cabre, Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi, J. Am. Math. Soc. 13, No. 4, (2000) 725-739. [7] V. Bargert, On minimal laminations on the torus, Ann. Inst. H. Poincar´e Anal. NonLin´eaire, 6 (1989), 95–138. T. F. Bass and C. Gui, The Liouville property and a conjecture of De Giorgi, Comm. Pure Appl. Math. 8, (2000) 1007-1038. [9] H. Berestycki, F. Hamel and R. Monneau, One-dimensional symmetry for some bounded entire solutions of some elliptic equations, Duke Math.