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We study the boundary value problem in , on , where is a smooth bounded domain in . Our attention is focused on two cases when , where for any or for any . In the former case we show the existence of infinitely many weak solutions for any . In the latter we prove that if is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a -symmetric version for even functionals...
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
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