1. Existence of solutions for the Dirichlet problem with superlinear nonlinearities Creator: Nowakowski, Andrzej and Rogowski, Andrzej Format: bez média and svazek Type: model:article and TEXT Subject: nonlinear Dirichlet problem, nontrivial solution, duality method, and superlinear nonlinearity Language: English Description: 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 $x$. Rights: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public