By the application of a technique developed by G. J. Butler we find infinitely many solutions of a Floquet-type BVP for the equation x''+q(t)g(x)=0, where q is a weight function that is allowed to change sign, g is is superlinear and such that g(x)x>0 for all non-zero x. The boundary condition is (x(b),x'(b))=L(x(a),x'(a)), where L is a continuous, positively homogeneous, and nondegenerate map. At first we apply the main result to obtain solutions with a prescribed large number of zeros when L is the rotation of a fixed angle l; second, we find infinitely many subharmonic solutions of any order and, again, solutions with a prescribed large number of zeros for the periodic problem associated to the equation x''+cx'+q(t)g(x)=0, with q and g as above and a constant c.

Papini, D. (2000). Infinitely many solutions for a Floquet-type BVP with superlinearity indefinite in sign. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 247(1), 217-235 [10.1006/jmaa.2000.6849].

Infinitely many solutions for a Floquet-type BVP with superlinearity indefinite in sign

PAPINI, DUCCIO
2000-01-01

Abstract

By the application of a technique developed by G. J. Butler we find infinitely many solutions of a Floquet-type BVP for the equation x''+q(t)g(x)=0, where q is a weight function that is allowed to change sign, g is is superlinear and such that g(x)x>0 for all non-zero x. The boundary condition is (x(b),x'(b))=L(x(a),x'(a)), where L is a continuous, positively homogeneous, and nondegenerate map. At first we apply the main result to obtain solutions with a prescribed large number of zeros when L is the rotation of a fixed angle l; second, we find infinitely many subharmonic solutions of any order and, again, solutions with a prescribed large number of zeros for the periodic problem associated to the equation x''+cx'+q(t)g(x)=0, with q and g as above and a constant c.
Papini, D. (2000). Infinitely many solutions for a Floquet-type BVP with superlinearity indefinite in sign. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 247(1), 217-235 [10.1006/jmaa.2000.6849].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/22990
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