Search results for "multiple solutions"

On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

2016

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Multiple solutions for a discrete boundary value problem involving the p-Laplacian.

2008

Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.

Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

2010

Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator

2020

Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.

An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities

2005

AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.

Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity

2008

AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.

Existence of three solutions for a quasilinear two point boundary value problem

2002

In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:¶¶ $ \left\{\begin{array}{ll} u'' + \lambda h(u')f(t,\:u) = 0\\ u(0) = u(1) = 0.\\\end{array}\right.\ $ ¶¶Our main tool is a recent three critical points theorem of B. Ricceri ([10]).

Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

2021

The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.

On Different Type Solutions of Boundary Value Problems

2016

We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].

Critical points for nondifferentiable functions in presence of splitting

2006

A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.