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On a nonresonance condition between the first and the second eigenvalues for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$"><mml:mi>p</mml:mi></mml:math>-Laplacian

On a nonresonance condition between the first and the second eigenvalues for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$"><mml:mi>p</mml:mi></mml:math>-Laplacian

We are concerned with the existence of solution for the Dirichlet problem − Δ p u = f ( x , u ) + h ( x ) in Ω , u = 0 on ∂ Ω , when f ( x , u ) lies in some sense between …