in this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. we use some natural constraints and the ljusternik-schnirelman critical point theory on c1-manifolds, to prove our main results.

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem related to plasma confinement. The associated energy functional is nondifferentiable, and therefore standard variational methods cannot be used directly to prove...

This paper is concerned with a system of nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping terms. It is well-known that the presence of a nonlinear boundary source causes significant difficulties since the linear Neumann problem for the single wave equation is not, in general, well-posed in the finite-energy space H(Ω) × L(∂Ω...

In this paper we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has singular and parametric superlinear term nonlinear Neumann boundary condition of critical growth. Based on new equivalent norm for Musielak-Orlicz Sobolev spaces Nehari manifold fibering method prove existence at least two weak solutions provided parameter is sufficiently sma...

Abstract In this paper, we study the following coupled Choquard system in : where and , which denotes if . The function is a Riesz potential. By using Nehari manifold method, obtain existence of positive ground state solution case bounded potential periodic potential, respectively. particular, nonlinear term includes well‐studied less‐studied Moreover, it seems to be first result for

In this article, we study the multiplicity of solutions for a class fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under appropriate assumption, prove that there are at least two equation by Nehari manifold Ekeland variational principle, one which is ground state solution.

This article consists of study anisotropic double phase problems with singular term and sign changing subcritical as well critical nonlinearity. Seeking the help known Nehari manifold technique, we establish existence at least two opposite energy solutions in case one negative solution case. The results are new also classical p-Laplacian

Abstract In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has combined effect of singular parametric term. Based on fibering method using Nehari manifold are going to prove existence at least two weak solutions for such problems when parameter is sufficiently small.