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Infinitely many solutions for ordinary $p$-Laplacian systems with nonlinear boundary conditions

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  • This paper deals with the existence of infinitely many solutions for the boundary value problem

    $-( | u' | ^{p-2}u')' + \varepsilon |u|^{p-2}u= \nabla F(t,u), $ in $(0,T)$,

    $((|u'|^{p-2}u')(0), $ $ -(|u'|^{p-2}u')(T))$ $\in \partial j(u(0), u(T)),$

    where $\varepsilon \geq 0$, $p \in (1, \infty)$ are fixed, the convex function $j:\mathbb R^N \times \mathbb R^N \to (- \infty , +\infty ]$ is proper, even, lower semicontinuous and $F:(0,T) \times \mathbb R^N \to \mathbb R $ is a Carathéodory mapping, continuously differentiable and even with respect to the second variable.

    Mathematics Subject Classification: Primary: 34B15, 34L30; Secondary: 49J40.


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