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This paper deals with the existence of infinitely many solutions for a new class of Schrödinger–Kirchhoff type equations of the form M([u]s,pp+∫RNV(x)|u|pdx)[(-Δ)psu+V(x)|u|p-2u]=λh(x)|u|q-2u+f(x,u),x∈RN,where [u]s,pp:=∬R2N|u(x)-u(y)|p|x-y|N+spdxdy,s∈ (0 , 1) , N> sp, p≥ 2 , M(t) = a- btγ-1, t≥ 0 , 1<γ0 with a,b∈R0+:=[0,∞), λ is a parameter, q∈ (1 , p) , (-Δ)ps is the fractional p-Laplace operator, V: RN→ R+: = (0 , ∞) is a potential function, h is a sign-changing weight function and f is a continuous function satisfying the Ambrosetti–Rabinowitz condition or not. To our best knowledge, the results here are the first contributions to the study of fractional... 

In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021...