Superlinear Boundary Value Problems Research Articles

RETRACTED ARTICLE: Existence results for the general Schr\xf6dinger\t\t\tequations with a superlinear Neumann boundary value problem

The main goal of this paper is to study the general Schrödinger\t\t\t\tequations with a superlinear Neumann boundary value problem in domains with conical\t\t\t\tpoints on the boundary of the bases. First the formulation and the complex form of\t\t\t\tthe problem for the equations are given, and then the existence result of solutions\t\t\t\tfor the above problem is proved by the complex analytic method and the fixed point\t\t\t\tindex theory, where we absorb the advantages of the methods in recent works and give\t\t\t\tsome improvement and development. Finally, we are also interested in the asymptotic\t\t\t\tbehavior of solutions of the mentioned equation. These results generalize some\t\t\t\tprevious results concerning the asymptotic behavior of solutions of non-delay\t\t\t\tsystems of Schrödinger equations or of delay Schrödinger equations.

Existence of nontrivial solutions for superlinear three-point boundary value problems

In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.

On a superlinear periodic boundary value problem with vanishing Green's function

On a superlinear periodic boundary value problem with vanishing Green's function

Existence of positive solutions fornth-orderp-Laplacian singular super-linear boundary value problems

This paper investigates the existence of positive solutions for n th-order ( n ≥ 3 ) p -Laplacian singular super-linear boundary value problems. A necessary and sufficient condition for the existence of S p n − 2 positive solutions as well as S p n − 1 positive solutions is given by means of the fixed point theorems on cones.

Multiplicity results for superlinear boundary value problems with impulsive effects

We study the existence and multiplicity of solutions for a nonlinear boundary value problem subject to perturbations of impulsive terms. Under suitable assumptions on the potential of the nonlinearity, the existence of one or two solutions is established. Our approach is based on a local minimum theorem and a two non‐zero critical points for differentiable functionals. Copyright © 2015 John Wiley & Sons, Ltd.

Extension of the example by Moore-Nehari

Abstract R. Moore and Z. Nehari developed the variational theory for superlinear boundary value problems of the form x'' = p(t) |x|2εx, x(a) = 0 = x(b), where ε > 0 and p(t) is a positive continuous function. They constructed simple example of the equation considered in the interval [0, b] so that the problem had three positive solutions. We show that this example can be extended so that the respective BVP has infinitely many groups of solutions with a presribed number of zeros.

Positive solutions for superlinear fractional boundary value problems

We establish the existence, uniqueness, and global behavior of a positive solution for the following superlinear fractional boundary value problem: D α u(x )= u(x)ϕ(x, u(x)), x ∈ (0, 1), limx→0+ D α-1 u(x )=- a, u(1) = b ,w here 1 0a ndϕ(x, t) is a nonnegative continuous function in (0, 1) × (0, ∞ )t hat is required to satisfy some appropriate conditions related to a certain class of functions Kα. Our approach is based on estimates of the Green's function and on perturbation arguments. MSC: 34A08; 34B18; 34B27

Global structure of positive solutions for superlinear discrete boundary value problems

Let be an integer with T>1, , . We consider discrete boundary value problems where , and f(s)>0 for s>0, and f 0 = ∞, where . We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.

Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition

We show the incompleteness of a usually used version of the generalized Ambrosetti–Rabinowitz condition in superlinear problems, also used in the paper cited in the title, and we propose a complete one.

Nonexistence and existence of multiple positive solutions for superlinear three-point boundary value problems via index theory

This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f(t, x, y) is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f(t, x, y) is superlinear in χ at +∞.

Existence of positive solutions for 2nth-order singular superlinear boundary value problems

This paper investigates the existence of positive solutions for 2 n th-order ( n > 1 ) singular superlinear boundary value problems. A necessary and sufficient condition for the existence of C 2 n − 2 [ 0 , 1 ] as well as C 2 n − 1 [ 0 , 1 ] positive solutions is given by constructing a special cone and with the e -Norm.

Existence of positive solutions for second-order semipositone differential equations on the half-line

In this paper, by means of constructing a special cone, we obtain a sufficient condition for the existence of positive solution for semipositone singular Sturm-Liouville boundary value problem on the half-line. The results obtained generalize and improve the corresponding results of Zhang and Liu in papers [X.G. Zhang, L.S. Liu, Positive solutions of superlinear semipositone singular Dirichlet boundary value problems, J. Math. Anal. Appl. 316 (2006) 525–537, Y.S. Liu, Existence and unboundedness of positive solutions for singular boundary value problems on half-line, Appl. Math. Comput. 144 (2003) 543–556].

Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem

We consider a general nonlinear elliptic problem of the second order whose associated functional presents two linking structures and we prove the existence of three nontrivial solutions to the problem.

Positive solutions of even higher-order singular superlinear boundary value problems

This paper investigates 2 m th-order ( m > 1) superlinear singular two-point boundary value problems and obtains some necessary and sufficient conditions for existence of C 2( m−1) or C 2 m−1 positive solutions on the closed interval.

Positive solutions of superlinear boundary value problems with singular indefinite weight

In the present paper, we propose a method to deal with non-ordered lower and upper solutions in the case of ODE's with singular coefficients. As an application, we study the existence of positive solutions for a two-point boundary value problem on]0, 1[ associated to the equation u + a(t)g(u) = 0, where the function g : R+ --> R+ is continuous with superlinear growth at infinity and the weight a(t) changes sign as well as it may present some singularities at t = 0 or t = 1.

Multiple solutions for a super-linear three-point boundary value problem

Multiple solutions for a super-linear three-point boundary value problem

Upper and lower solutions method and a singular superlinear boundary value problem for the one-dimensional p-Laplacian

The singular boundary value problem ▪ is studied in this paper where Φ( s) = ⋎ s⋎ p−2 s, p > 1. The singularity may appear at u = 0, t = 0, and t = 1, and the function g may be superlinear at u = ∞ and change sign. The existence of solutions is obtained via an upper and lower solutions method.

Multiplicity of solutions for a class of nonsymmetric eigenvalue hemivariational inequalities

The aim of this paper is to establish the influence of a non-symmetric perturbation for a symmetric hemivariational eigenvalue inequality with constraints. The original problem was studied by Motreanu and Panagiotopoulos who deduced the existence of infinitely many solutions for the symmetric case. In this paper it is shown that the number of solutions of the perturbed problem becomes larger and larger if the perturbation tends to zero with respect to a natural topology. Results of this type in the case of semilinear equations have been obtained in [1] Ambrosetti, A. (1974), A perturbation theorem for superlinear boundary value problems, Math. Res. Center, Univ. Wisconsin-Madison, Tech. Sum. Report 1446; and [2] Bahri, A. and Berestycki, H. (1981), A perturbation method in critical point theory and applications, Trans. Am. Math. Soc. 267, 1–32; for perturbations depending only on the argument.

Varying bifurcation diagrams of positive solutions for a class of indefinite superlinear boundary value problems

In this work we analyze the existence, multiplicity and stability of positive solutions for a class of indefinite superlinear elliptic boundary value problems. The main contribution of this paper consists in the change of mind inherent to the fact of adding the superlinear amplitude e as an unfolding parameter. This change of mind allows us to unify many previous results obtained separately in the literature, it helps us to realize the global structure of the set of positive steady states, and provides us with a great variety of new general results. Our techniques can be applied to much more general equations and systems.

Discrete systems on infinite intervals

We study superlinear boundary value problems for a discrete system which in particular includes the prototype equation x( k + 1) = f( k, x( k)), equations with finite as well as infinite delays, equations of neutral type, and the discrete integral equations of Volterra type.