Periodic solutions of nonlinear second-order differential equations which are not solvable for the highest derivative

DOI10.1016/0022-247X(82)90113-5zbMath0516.34019MaRDI QIDQ1052507

J. Blot

Publication date: 1982

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

generalized solutionsdegree theorysemilinear equationsA-proper mappings

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) General theory for ordinary differential equations (34A99)

Related Items (17)

On the solvability of an equation describing the periodic motions of a satellite in its elliptic orbit ⋮ Topological degree and A-proper operators ⋮ On the solvability of a Neumann boundary value problem for the differential equation \(f(t,x,x',x)=0\) ⋮ Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition ⋮ A priori bounds and nodal properties for periodic solutions to a class of ordinary differential equations ⋮ Periodic solutions of certain higher order nonlinear differential equations ⋮ Existence theorems for higher order nonlinear periodic boundary value problems ⋮ On a singular boundary value problem for the differential equation \(f(t,x,x^{\prime },x^{\prime\prime })=0 \) using barrier strips ⋮ A generalized-degree homotopy yielding global bifurcation results ⋮ Sufficient conditions for periodic solutions to a class of second-order differential equations ⋮ A fixed-point index and existence theorems for semilinear equations in cones ⋮ Existence and uniqueness of initial value problems for a class of second- order differential equations ⋮ An application of A-mapping theory to boundary value problems for ordinary differential equations ⋮ Global bifurcation of a class of periodic boundary-value problems ⋮ Boundary value problems at resonance for certain semilinear ordinary differential equations ⋮ Solvability of Neumann BV problems for nonlinear second-order ODEs which need not be solvable for the highest-order derivative ⋮ Sharp non-resonance conditions for periodically perturbed Liènard systems

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