On the second order equations with nonlinear impulses - Fredholm alternative type results

Pavel Drábek, Martina Langerová

Abstract


We consider the semilinear homogeneous Dirichlet boundary value problem for the second order equation
on a finite interval with nonlinear impulses in the derivative at prescribed points. We introduce
Landesman-Lazer type necessary and sufficient conditions for resonance problems and generalize
the Fredholm alternative results for linear operators. An interaction between nonlinear
restoring force and nonlinear impulses is presented.

Keywords


Ordinary differential equations of the second order with impulses; resonance problems; Landesman-Lazer conditions

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