### On the existence of two solutions for a general class of jumping problems

DOI: http://dx.doi.org/10.12775/TMNA.2003.020

#### Abstract

Via nonsmooth critical point theory we prove the existence

of at least two solutions in $W^{1,p}_0(\Omega)$

for a jumping problem involving the Euler

equation of multiple integrals of calculus of variations

under natural growth conditions. Some new difficulties

arise in comparison with the study of the semilinear and also

the quasilinear case.

of at least two solutions in $W^{1,p}_0(\Omega)$

for a jumping problem involving the Euler

equation of multiple integrals of calculus of variations

under natural growth conditions. Some new difficulties

arise in comparison with the study of the semilinear and also

the quasilinear case.

#### Keywords

Jumping problems; quasilinear problems; critical point theory

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