Geodesic
Existence of solutions for the Dirichlet problem with superlinear nonlinearities
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 515-528.

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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 $x$.
Classification : 34B15, 47J30, 49J40
Keywords: nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity 
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     author = {Nowakowski, Andrzej and Rogowski, Andrzej},
     title = {Existence of solutions for the {Dirichlet} problem with superlinear nonlinearities},
     journal = {Czechoslovak Mathematical Journal},
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     volume = {53},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a1/}
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Nowakowski, Andrzej; Rogowski, Andrzej. Existence of solutions for the Dirichlet problem with superlinear nonlinearities. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 515-528. http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a1/