Differential equations whose solution of the Cauchy problem displays nonclassical behaviour with respect to the parameter {lambda}

Journal Article · Sat Oct 31 04:00:00 EDT 2009 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2009V200N10ABEH004050; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21301426

Yakubov, Vladimir Ya ^[1]

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1. Moscow State Institute of Electronics and Mathematics (Technical University), Moscow (Russian Federation)

The behaviour of solutions of the equation y''+{lambda}{rho}(x,{lambda})y=0 with respect to the spectral parameter {lambda} is investigated under the assumption that the function {rho}(x,{lambda}) does not satisfy the classical conditions. Two types of equations are considered: the Sturm-Liouville equation y''+{lambda}{rho}(x)y=0, whose solutions grow like c({rho}){lambda}{sup m} in the norm of C[0,l] (where m>0 is arbitrary), and equations of the form y''+{lambda}{rho}(x,{lambda})y=0, lim {sub {lambda}}{sub {yields}}{sub +{infinity}}{rho}(x,{lambda})=1, whose solutions can grow like c{lambda}{sup m} in the norm of C[0,l] (where m>0 is arbitrary) and even like exp{l_brace}m{lambda}{sup 1-{gamma}}{r_brace} where 0<{gamma}<1. Bibliography: 3 titles.

• OSTI ID: 21301426
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 10 Vol. 200; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
CAUCHY PROBLEM
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
STURM-LIOUVILLE EQUATION