Published 2022-06-01
“…In this paper, a special class of
boundary value problems, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mo>▵</mo><mi>u</mi><mo>=</mo><mi>λ</mi><msup><mi>u</mi><mi>q</mi></msup><mo>+</mo><msup><mi>u</mi><mi>r</mi></msup><mo>,</mo><mi>in</mi><mspace width="4pt"></mspace><mi mathvariant="sans-serif">Ω</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>in</mi><mspace width="4pt"></mspace><mi mathvariant="sans-serif">Ω</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold">n</mi><mo>·</mo><mo>∇</mo><mi>u</mi><mo>+</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>on</mi><mspace width="4pt"></mspace><mo>∂</mo><mi mathvariant="sans-serif">Ω</mi><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>0</mn><mo><</mo><mi>q</mi><mo><</mo><mn>1</mn><mo><</mo><mi>r</mi><mo><</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></mrow></mstyle></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>→</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula> is a nondecreasing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mn>1</mn></msup></semantics></math></inline-formula> function. …”
Get full text
Article