Related papers: A Nehari manifold method for nonvariational proble…

This paper develops a fixed point version of the well-known Nehari manifold method from critical point theory. The main result is formulated for systems of operator equations, relying on the fixed point theorems of Schauder and Schaefer.…

Using the Nehari manifold method, we establish sufficient conditions such that a smooth functional attains a ground state within an annular domain of a closed cone. The localization we obtain immediately allows for multiplicity when applied…

This paper is concerned with a singular multi-phase problem with variable singularities. The main tool used is the Nehari manifold approach. Existence of at least two positive solutions with positive-negative energy levels are obtained.

In this paper, we deal with equations of variational form which Nahari manifolds can contain more than two different types of critical points. We introduce a method of separating critical points on the Nahari manifold, based on the use of…

In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: \begin{equation*} \;\;\; \begin{array}{rl}…

In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of…

This paper is concerned with multiplicity results for parametric singular double phase problems in $\mathbb{R}^N$ via the Nehari manifold approach. It is shown that the problem under consideration has at least two nontrivial weak solutions…

In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such…

The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply the nonlinear generalized Rayleigh quotient method.

We prove the existence, multiplicity, and bifurcation of solutions with prescribed energy for a broad class of scaled problems by introducing a suitable notion of scaling based Nehari manifold. Applications are given to…

This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, and depend on the real parameter $\lambda$. A special focus is…

In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.

The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison…

We establish the existence of a nonnegative fully nontrivial solution to a non-variational weakly coupled competitive elliptic system. We show that this kind of solutions belong to a topological manifold of Nehari-type, and apply a…

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at…

In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the…

In this article, we study the existence and multiplicity of non-negative solutions of following $p$-fractional equation: $$ \quad \left\{\begin{array}{lr}\ds \quad - 2\int_{\mb R^n}\frac{|u(y)-u(x)|^{p-2}(u(y)-u(x))}{|x-y|^{n+p\al}} dxdy =…

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…

Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…

In this paper we study the existence and multiplicity of two distinct nontrivial weak solutions of the following equation in Nehari manifold. We have also proved that these solutions are in $L^{\infty}(\Omega)$. \begin{align*} \begin{split}…