Sign-changing Weight Function Research Articles

Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions

In this paper, we study the elliptic problem where is the critical Sobolev exponent, and or is a sign-changing function. Under different assumptions on and we prove the existence of infinitely many solutions to the above problem. We also show that one of these solutions is positive.

Elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions

In this article we establish the existence and nonexistence of a weak solution to singular elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions.

Existence of multiple solutions for an elliptic system with sign-changing weight functions

In this paper, we will consider a class of quasilinear elliptic problem of the form {−div(|x|−ap|∇u|p−2∇u)+g1(x)|u|p−2u=αα+βh(x)|u|α−2u|v|β+λH1(x)|u|n−2u,−div(|x|−ap|∇v|p−2∇v)+g2(x)|v|p−2v=βα+βh(x)|v|β−2v|u|α+μH2(x)|v|n−2v,u(x)>0,v(x)>0,x∈RN, where λ, μ>0, 1<p<N, 1<n<p<α+β<p∗=NpN−pd, 0≤a<N−pp, a≤b<a+1, d=a+1−b>0, the weight g1(x), g2(x) are bounded and nonnegative functions and h(x), H1(x), H2(x) are continuous functions which change sign in RN. We will prove that the problem has at least two positive solutions by using the Nehari manifold and the fibering maps associated with the Euler function for this problem.

The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system (Eλ,μ) involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of R2.

On the p-biharmonic equation involving concave-convex nonlinearities and sign-changing weight function

In this paper, we study the combined effect of concave and convex nonlinearities on the number of nontrivial solutions for the p-biharmonic equation of the form � � 2 u = j uj q−2 u + �f(x)j uj r−2 u in , u = r u = 0 on @,

Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Let Ω∋0 be an-open bounded domain in ℝ𝑁(𝑁≥3) and 𝑝∗=(𝑝𝑁/(𝑁−𝑝)). We consider the following quasilinear elliptic system of two equations in 𝑊01,𝑝(Ω)×𝑊01,𝑝(Ω): −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢

Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions

This article shows the existence and multiplicity of positive solutions of the -Laplacian problem where is a bounded open set in with smooth boundary and are continuous functions on such that and are smooth functions which may change sign in . The method is based on Nehari results on three sub-manifolds of the space .

Multiplicity of positive solutions for critical singular elliptic systems with sign-changing weight function

Multiplicity of positive solutions for critical singular elliptic systems with sign-changing weight function

Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms

In this paper, we are concerned with the following quasilinear elliptic equation where Ω ⊂ ℝ N is a smooth domain with smooth boundary ∂Ω such that 0 ∈ Ω, Δ p u = div(|∇u|p-2∇u), 1 < p < N, , λ > 0, 1 < q < p, sign-changing weight functions f and g are continuous functions on , is the best Hardy constant and is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solutions to this equation is verified.

The Nehari manifold for a degenerate elliptic equation involving a sign-changing weight function

This paper is concerned with a degenerate elliptic equation of the form { − div ( | x | − 2 a ∇ u ) = | x | − 2 b | u | p − 1 u + λ f ( x ) | x | − 2 c | u | q − 1 u in Ω , u = 0 on ∂ Ω , where Ω ⊂ R N ( N ≥ 3 ) is an open bounded domain with smooth boundary, 0 ∈ Ω , 0 < a < N − 2 2 , a ≤ b , c < a + 1 and b = c ( p + 1 ) q + 1 , f ∈ C ( Ω ¯ ) be a sign-changing weight function. Using the Nehari manifold and a fibering map, the existence of multiple nonnegative solutions is established.

Three positive solutions for a semilinear elliptic equation in [formula omitted] involving sign-changing weight

In this paper, we study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result and the Lusternik–Schnirelmann category to prove that a semilinear elliptic equation in R N involving sign-changing weight function has at least three positive solutions.

Existence of two solutions for a Navier boundary value problem involving the p-biharmonic

In this paper, we study the Navier boundary value problem involving the p-biharmonic system with sign-changing weight function. By using the Nehari manifold and variational meth- ods, the existence of two nontrivial solutions is obtained when the pair of the parameters (λ ,μ) belongs to a certain subset of R 2 .

Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions

Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems $$ \cases{\displaystyle -{\mit\Delta}_p u+|u|^{p-2}u=f_{1\lambda_1}(x) |u|^{q-2 }u+\frac{2\alpha}{\alpha+\beta}g_\mu|u|^{\alpha-2}u|v|^\beta,\qu

The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions

This paper examines a class of Kirchhoff type equations that involve sign-changing weight functions. Using Nehari manifold and fibering map, the existence of multiple positive solutions is established.

Three positive solutions for Dirichlet problems involving critical Sobolev exponent and sign-changing weight

In this paper, we study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result and the Lusternik–Schnirelman category to prove that a semilinear elliptic equation involving a sign-changing weight function has at least three positive solutions.

On existence of positive solutions for a class of Caffarelli–Kohn–Nirenberg type equations

We investigate the solvability of a singular equation of Caffarelli&#8211;Kohn&#8211;Nirenberg type having a <i>critical-like</i> nonlinearity with a sign-changing weight function. We shall examine how the properties of the Nehari manifold and the fiberi

Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition

In this paper, we study a class of semilinear elliptic equations in $R_+^N$ with nonlinear boundary condition and sign-changingweight function. By means of the Lusternik-Schnirelman category,multiple positive solutions are obtained.

A fibering map approach to a potential operator equation and its applications

In this paper, we study the existence of multiple solutions for operator equations involving homogeneous potential operators. With the help of the Nehari manifold and the fibering method, we prove that some such equations have at least two nonzero solutions. Furthermore, we apply this result to prove the existence of two positive solutions for some quasilinear elliptic problems involving sign-changing weight functions.

Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic equation with sign-changing weight functions. With the help of the Nehari manifold, we prove that there are at least two solutions for the equation (Ea,b).

Multiple positive solutions for semilinear Dirichlet problems with sign-changing weight function in infinite strip domains

In this paper, existence and multiplicity results to the following Dirichlet problem { − Δ u + u = λ f ( x ) | u | q − 1 + h ( x ) | u | p − 1 , in Ω u > 0 , in Ω u = 0 , on ∂ Ω are established, where Ω = Ω ′ × R , Ω ′ ⊂ R N − 1 is bounded smooth domain and N ≥ 2 . Here 1 < q < 2 < p < 2 ∗ ( 2 ∗ = 2 N N − 2 if N ≥ 3 , 2 ∗ = ∞ if N = 2 ) , λ is a positive real parameter, the function f , among other conditions, can possibly change sign in Ω , and the function h satisfies suitable conditions. The study is based on the comparison of energy levels on Nehari manifold.