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• W2000855114 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi mathvariant=double-struck>T</mml:mi><mml:mo>⊂</mml:mo><mml:mi mathvariant=double-struck>R</mml:mi></mml:math>be a periodic time scale in shifts<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math>with period<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>P</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant=normal>∞</mml:mi><mml:msub><mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=double-struck>T</mml:mi></mml:mrow></mml:msub></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mi mathvariant=double-struck>T</mml:mi></mml:math>is nonnegative and fixed. By using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive solutions in shifts<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math>for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form:<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>Δ</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo><mml:mo>, </mml:mo><mml:mi>t</mml:mi><mml:mo>≠</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>, </mml:mo><mml:mi>t</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=double-struck>T</mml:mi><mml:mo>, </mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=false>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo><mml:mo>,</mml:mo></mml:math>where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>×</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>is a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the results." @default.
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• W2000855114 title "Positive Periodic Solutions in Shiftsδ±for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales" @default.
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• W2000855114 doi "https://doi.org/10.1155/2014/509052" @default.
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