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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MR Zbl
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 $x$.
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 
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/
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