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Existence of Solutions for the Dirichlet Problem with Superlinear Nonlinearities

Authors:

Andrzej Nowakowski Andrzej Rogowski

Institution:

(1) Faculty of Mathematics, University of Lstrok

ód

, Banacha 22, 90-238 Lstrok

ód

, Poland

Abstract:

In this paper we establish the existence of nontrivial solutions to

$\frac{d}{{dt}}L_{x'} \left( {t,x'\left( t \right)} \right) + {\text{V}}_x \left( {t,x\left( t \right)} \right) = 0,x\left( 0 \right) = x\left( T \right)$

with V _x superlinear in x.

Keywords:

nonlinear Dirichlet problem nontrivial solution duality method superlinear nonlinearity

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