The Mawhin Operator

Robert F. Brown
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Robert F. Brown: University of California, Department of Mathematics

Chapter 12 in A Topological Introduction to Nonlinear Analysis, 2004, pp 79-84 from Springer

Abstract: Abstract In Chapter 5 we saw that if e: R → R is an odd, T-periodic function, then the forced pendulum equation with forcing term e, that is, $$ y'' + a \sin y = e, $$ always has a solution y: R → R that is also an odd, T-periodic function. Remember how we constructed that solution: we built it up out of copies of a solution $$ y:[0,\tfrac{T} {2}] \to R $$ to the Dirichlet boundary value problem corresponding to that differential equation, that is, with the boundary condition $$ y(0) = y(\tfrac{T} {2}) = 0 $$ .

Keywords: Linear Space; Null Space; Force Term; Finite Subset; Fredholm Operator (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8124-1_12

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