Existence and multiplicity of solutions to concave–convex-type double-phase problems with variable exponent

Existence of weak solutions for Kirchhoff type double‐phase problem in ℝ

“…They also obtained an existence result for a problem involving a convection term. For some more existence results, we refer to the works of Aberqi et al [16] (a problem on complete manifold), Kim et al [17] (convex-concave nonlinearities), Guarnotta et al [18] (system with convection term), Vetro and Winkert [19], Arora and Dwivedi [20] (singular nonlinearity), and Ho and Winkert [21] (for Kirchhoff type) and Ho and Winkert [22](embedding results and a priori bounds).…”

Existence and multiplicity of solutions for (p,q)$$ \left(p,q\right) $$‐Laplacian Kirchhoff‐type fractional differential equations with impulses

“…However, there are still some nonlinearities that do not satisfy either the (AR)-condition or (MS)-condition, thus limiting the widespread use of the variational method. For instance, Kim et al [26] gave the following example:…”

“…However, there are still some nonlinearities that do not satisfy either the (AR)‐condition or (MS)‐condition, thus limiting the widespread use of the variational method. For instance, Kim et al [26] gave the following example: $$$$ f\left(x,t\right)=\sigma (x)\left({\left|t\right|}^{p-2}t+\frac{2}{p}\sin t\right), $$$$ where $$$ x\in \Omega, \sigma \in {L}^{\infty}\left(\Omega \right) $$$.…”

Infinitely many solutions to Kirchhoff double phase problems with variable exponents

“…In this case, only few and very recent results exist. We refer to the papers of Aberqi-Bennouna-Benslimane-Ragusa [1], Bahrouni-Rȃdulescu-Winkert [5], Crespo-Blanco-Gasiński-Harjulehto-Winkert [10], Kim-Kim-Oh-Zeng [20] , Leonardi-Papageorgiou [22], Vetro-Winkert [26] and Zeng-Rȃdulescu-Winkert [28].…”