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nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity
In this paper we establish the existence of nontrivial solutions to \[\frac{\mathrm d}{{\mathrm d}t}L_{x^{\prime }}(t,x^{\prime }(t))+V_{x} (t,x(t))=0,\quad x(0)=0=x(T),\] with $V_x$ superlinear in $x$.
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