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- W2104996923 abstract "We are concerned with the existence of solution for the Dirichlet problem<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$- triangle_p u = f(x,u) + h(x)$><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>Δ</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Omega$><mml:mi>Ω</mml:mi></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$u = 0$><mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$partialOmega$><mml:mrow><mml:mo>∂</mml:mo><mml:mi>Ω</mml:mi></mml:mrow></mml:math>, when<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$f(x,u)$><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>lies in some sense between the first and the second eigenvalues of the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$p$><mml:mi>p</mml:mi></mml:math>-Laplacian<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$triangle_p$><mml:mrow><mml:msub><mml:mi>Δ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math>. Extensions to more general operators which are<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$(p - 1)$><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-homogeneous at infinity are also considered." @default.
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- W2104996923 date "2001-01-01" @default.
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- W2104996923 title "On a nonresonance condition between the first and the second eigenvalues for thep-Laplacian" @default.
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