In this paper, we are concerned with the existence of nonnegative solutions for a pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si1.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=2a41752479b1b9e1707560a10df81bb7" title="Click to view the MathML source">p-Kirchhoff type problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary data. As a particular case, we study the following problem
where is a fractional pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si1.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=2a41752479b1b9e1707560a10df81bb7" title="Click to view the MathML source">p-Laplace operator, pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si6.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=bded4382214a4f41eafc0f8fb4b31f3a" title="Click to view the MathML source">Ω is an open bounded subset of pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si7.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=ddb6804023df14bbefac2dbf63ab3c8f" title="Click to view the MathML source">RN with Lipschitz boundary, is a continuous function and is a continuous function satisfying the Ambrosetti–Rabinowitz type condition. The existence of nonnegative solutions is obtained by using the Mountain Pass Theorem and an iterative scheme. The main feature of this paper lies in the fact that the Kirchhoff function pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si10.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=d1a6b4fd82315c66a7df026e7951dd62" title="Click to view the MathML source">M depends on pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si11.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=eae27f853e81016a498ff365d440ef23" title="Click to view the MathML source">x∈Ω and the nonlinearity pport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089812211500560X&_mathId=si12.gif&_user=111111111&_pii=S089812211500560X&_rdoc=1&_issn=08981221&md5=b61d1151d2128a78005ec6aadfcb785c" title="Click to view the MathML source">f depends on the energy of solutions.