Hybrid Differential Inclusion Involving Two Multi-Valuedoperators with Nonlocal Multi-Valued Integral Condition

The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>∈</mo><msubsup><mo>∫</mo><mn>0</mn><mi>σ</mi></msubsup><mo>Δ</mo><mfenced separators="" open="(" close=")"><mi>s</mi><mo>,</mo><mi>η</mi><mo>(</mo><mi>s</mi><mo>)</mo></mfenced><mi>d</mi><mi>s</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> is a multi-valued map. Relative compactness of the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mo>∫</mo><mn>0</mn><mi>σ</mi></msubsup><mo>Δ</mo><mfenced separators="" open="(" close=")"><mi>s</mi><mo>,</mo><mi>η</mi><mo>(</mo><mi>s</mi><mo>)</mo></mfenced><mi>d</mi><mi>s</mi></mrow></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mn>2</mn></msup><mfenced separators="" open="(" close=")"><mo>(</mo><mn>0</mn><mo>,</mo><mi>ε</mi><mo>)</mo><mo>,</mo><mi mathvariant="double-struck">R</mi></mfenced></mrow></semantics></math></inline-formula> is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.