Multiplicity of Positive Solutions for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Laplacian Type Equation with Critical Nonlinearities
Multiplicity of Positive Solutions for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Laplacian Type Equation with Critical Nonlinearities
We study the effect of the coefficient<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>of the critical nonlinearity on the number of positive solutions for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Laplacian equation. Under suitable assumptions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mi>g</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, we should prove that for sufficiently small<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mi>λ</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:math>, there exist …