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The existence of a solution for Dirichlet boundary value problem for a Duffing type differential inclusion

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  • We consider a differential inclusion which is somehow analogous to the classical Duffing's equation with Dirichlet boundary condition. We prove the existence of a solution using two-steps approach. Firstly we consider an auxiliary problem where we substitute $h := \frac{dx} {dt} \in L^2(0,1)$. Next, using the method of pseudomonotone and coercive operators, we prove the existence of a solution to the auxiliary problem. Finally we prove that under suitable assumptions, an iterative scheme converges to the solution of our inclusion, which appears to be unique.
    Mathematics Subject Classification: Primary: 49K15; Secondary: 34B15.


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