Geodesic
Existence results for a class of high order differential equation associated with integral boundary conditions at resonance
Archivum mathematicum, Tome 53 (2017) no. 2, pp. 111-130
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By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form $$x^{(n)} =f(t,x,x^{\prime },\dots ,x^{(n-1)})\,, \quad t \in [0, 1]\,,$$ associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.
By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form $$x^{(n)} =f(t,x,x^{\prime },\dots ,x^{(n-1)})\,, \quad t \in [0, 1]\,,$$ associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.
DOI : 10.5817/AM2017-2-111
Classification : 34B10, 34B15
Keywords: coincidence degree; high order differential equation; resonance 
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Nhan, Le Cong; Hoang, Do Huy; Truong, Le Xuan. Existence results for a class of high order differential equation associated with integral boundary conditions at resonance. Archivum mathematicum, Tome 53 (2017) no. 2, pp. 111-130. doi: 10.5817/AM2017-2-111

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