Existence of three solutions for a three-point boundary value problem via a three-critical-point theorem

2015 ◽  
Vol 31 (2) ◽  
pp. 213-220
Author(s):  
XIAOJIE LIN ◽  
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Reflexive Banach Space ◽  
Boundary Value ◽  
Main Tool ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Critical Point Theorem

In this paper, we study the existence of at least three solutions for a three-point boundary value problem. By constructing and showing an appropriate separable and reflexive Banach space, a new multiplicity result of the three-point boundary value problem is established. Our main tool is based upon variational method and three-critical-point theorem.

scholarly journals Perturbations near resonance for thep-Laplacian inℝN

2002 ◽  
Vol 7 (6) ◽  
pp. 323-334 ◽  
Author(s):  
To Fu Ma ◽  
Maurício Luciano Pelicer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Principal Eigenvalue ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Laplacian Equation ◽  
Near Resonance

We study a multiplicity result for the perturbedp-Laplacian equation−Δpu−λg(x)|u|p−2u=f(x,u)+h(x) in ℝN, where1<p<Nandλis nearλ 1, the principal eigenvalue of the weighted eigenvalue problem−Δpu=λg(x)|u|p−2uinℝN. Depending on which sideλis fromλ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.

scholarly journals Three Solutions for Inequalities Dirichlet Problem Driven byp(x)-Laplacian-Like

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhou Qing-Mei ◽  
Ge Bin
Keyword(s):  
Dirichlet Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Critical Point Theorem ◽  
Nonlinear Elliptic ◽  
Locally Lipschitz

A class of nonlinear elliptic problems driven byp(x)-Laplacian-like with a nonsmooth locally Lipschitz potential was considered. Applying the version of a nonsmooth three-critical-point theorem, existence of three solutions of the problem is proved.

scholarly journals Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 526
Author(s):  
Ehsan Pourhadi ◽  
Reza Saadati ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

scholarly journals SOME MULTIPLICITY RESULTS TO THE EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET BOUNDARY VALUE PROBLEM INVOLVING THE P-LAPLACIAN

2011 ◽  
Vol 16 (3) ◽  
pp. 390-400 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem Alizadeh Afrouzi
Keyword(s):  
Boundary Value Problem ◽  
Critical Points ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Main Tool ◽  
Dirichlet Boundary Value Problem ◽  
Positive Real ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Uniformly Bounded

In this paper we prove the existence of two intervals of positive real parameters λ for a Dirichlet boundary value problem involving the p-Laplacian which admit three weak solutions, whose norms are uniformly bounded with respect to λ belonging to one of the two intervals. Our main tool is a three critical points theorem due to G. Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim., 28:249–258, 2004].

scholarly journals Solvability of a Class of Higher-Order Fractional Two-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Green's Function ◽  
Point Theorem ◽  
Caputo Derivative ◽  
Boundary Value ◽  
Higher Order ◽  
Sufficient Condition ◽  
Point Boundary

This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results. First, Green’s function of the considered BVP is obtained by using the property of Caputo derivative. Second, based on Schaefer’s fixed point theorem, the solvability of the considered BVP is studied, and a sufficient condition is presented for the existence of at least one solution. Finally, an illustrative example is given to support the obtained new results.

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