This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

In this paper, we study the multiplicity of positive solutions for the p-Laplacian problems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic equation has at least two positive solutions.

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation

In this article, we study periodic solutions of a class of delay differential equations. By restricting our discussion on generalized Nehari Manifold, some sufficient conditions are obtained to guarantee the existence of infinitely many pairs of periodic solutions. Also, there exists at least one periodic solution with prescribed minimal period.

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

−ε2∆u + V (x)u + ψu = f(u) in R, −ε2∆ψ = u in R, u > 0, u ∈ H(R), has been studied extensively, where the assumption for f(u) is that f(u) ∼ |u|p−2u with 4 < p < 6 and satisfies the Ambrosetti–Rabinowitz condition which forces the boundedness of any Palais– Smale sequence of the corresponding energy functional of the equation. The more difficult critical case is studied in this paper. As g(u) :...

We extend the results of [2] by computing conformal maps onto the canonical slit domains in Nehari [14]. Along the way, we demonstrate the computability of solutions to Neuman problems.

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Gehring and Pommerenke have shown that if the Schwarzian derivative S f of an analytic function f in the unit disk D satisfies ISf(z)] ~_ 2(1 I z [2 ) -2, then f (D) is a Jordan domain except when f (D) is the image under a M6bius transformation of an infinite parallel strip. The condition ISf(z)l <_ 2(1 lzl2) -2 is the classical sufficient condition for univalence of Nehari. In this paper we s...