Sign-changing Nonlinearity Research Articles

Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced argumentsDαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and η∈(0,1),whereDαis the standard Riemann-Liouville derivative,f:[0,∞)→[0,∞)is continuous,f(0)>0, h :[0,1]→(−∞,+∞), anda(t)is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.

Positive solutions for third-order p-Laplacian m-point boundary value problems with sign changing nonlinearity on time scales

Positive solutions for third-order p-Laplacian m-point boundary value problems with sign changing nonlinearity on time scales

Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities

Using the mountain pass theorem combined with the minimum principle, we obtain at least two non-negative, non-trivial weak solutions for a class of p(x)-Kirchhoff-type equations.

Existence and Multiplicity of Radial Positive Solutions for a Quasilinear Elliptic Equation with Sign-Changing Nonlinearity

In this paper we will be concerned with questions of existence and multiplicity of radial nonnegative solutions of the quasilinear elliptic equation [Figure not available: see fulltext.] We will use variational methods in order to prove the existence of multiple solutions in case f is a sign-changing nonlinearity.

Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales

In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated.MSC:34B10, 39A10.

Existence of multiple positive solutions for a nonlocal boundary value problem with sign changing nonlinearities

In this paper, we study the existence of multiple positive solutions for a nonlocal boundary value problem where the nonlinear term ƒ is allowed to change sign. We obtain at least two positive solutions by using a fixed point theorem in double cones.

Multiple solutions for singular N-Laplace equations with a sign changing nonlinearity

In this article, we prove the existence of multiple weak solutions to N-Laplace equation\begin{eqnarray}-\Delta_N u-\mu \frac{g(x)}{(|x| \log\frac{R}{|x|})^N }|u|^{N-2}u=\lambda f(x,u), \ in\ \Omega.\\u =0, \ on\ \partial \Omega,\end{eqnarray}using Bonanno's three critical point theorem.

Positive solutions to singular boundary value problems for fractional functional differential equations with changing sign nonlinearity

In this work, a boundary value problem is discussed for a singular delay differential equation of fractional order. The nonlinearity may change sign. By means of the Krasnoselskii fixed point theorem, existence results for positive solutions are obtained. Examples illustrating our main results are also given.

The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities

We investigate the existence of at least two positive solutions to eigenvalue problems of fractional differential equations with sign changing nonlinearities in more generalized boundary conditions. Our analysis relies on the Avery‐Peterson fixed point theorem in a cone. Some examples are given for the illustration of main results.

Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity

We discuss the existence of positive solutions to the following fractional m‐point boundary value problem with changing sign nonlinearity , where λ is a positive parameter, 1 < α ≤ 2, 0 < β < α − 1, 0 < ξ1 < ⋯<ξm−2 < 1 with , is the standard Riemann‐Liouville derivative, f and may be singular at t = 0 and/or t = 1 and also may change sign. The work improves and generalizes some previous results.

Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii′s fixed point theorem in a cone.

Standing waves for discrete nonlinear Schrödinger equations: sign-changing nonlinearities

We consider the discrete nonlinear Schrödinger equation with infinitely growing potential and sign-changing power nonlinearity. Making use of critical point theory, we prove an existence and multiplicity result for standing wave solutions.

Positive solutions for third-order boundary value problems with change of signs

In this paper, we study the third-order triple-point nonlinear boundary value problems with sign changing nonlinearities by employing Krasnoselkii–Guo fixed point theorem and Avery–Henderson fixed point theorem,and establish results on the existence of at least one or two positive solutions to the boundary value problems.

Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity

In this paper, we discuss the existence of positive solutions to the following fractional boundary value problem with changing sign nonlinearity. { D 0 + α u ( t ) + λ f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ′ ( 0 ) = u ( 1 ) = 0 , where 2 < α ≤ 3 is a real number, D 0 + α is the standard Riemann–Liouville derivative, λ is a positive parameter, f may change sign and may be singular at t = 0 , 1 .

A Variational Approach to a Nonlocal Elliptic Problem with Sign-Changing Nonlinearity

Abstract In this paper we are concerned with the nonlocal elliptic problem where Ω ⊂ℝN is a bounded smooth domain, f, g : ℝ →ℝ are given functions and p is a fixed real number. We use variational methods to prove multiplicity results.

Breather solutions of the discrete nonlinear Schrödinger equations with sign changing nonlinearity

In this paper, we investigate the breather solutions of the discrete nonlinear Schrödinger equation with the unbounded potential and nonlinearity containing both self-focusing and defocusing sites (which means the coefficients of nonlinearity change sign). By using the generalized Nehari manifold method, we obtain the existence of nontrivial exponential decay breather solutions.

Monotonicity and one-dimensional symmetry for solutions of −Δ p u = f(u) in half-spaces

We prove a weak comparison principle in narrow domains for sub-super solutions to −Δpu = f(u) in the case 1 < p ≤ 2 and f locally Lipschitz continuous. We exploit it to get the monotonicity of positive solutions to −Δpu = f(u) in half spaces, in the case \({\frac{2N+2}{N+2} < p\leq 2}\) and f positive. Also we use the monotonicity result to deduce some Liouville-type theorems. We then consider a class of sign-changing nonlinearities and prove a monotonicity and a one-dimensional symmetry result, via the same techniques and some general a-priori estimates.

Compactly supported solutions for a semilinear elliptic problem in ℝn with sign-changing function and non-Lipschitz nonlinearity

For a sign-changing function a(x) we consider the solutions of the following semilinear elliptic problem in ℝn with n ≥ 3:where γ &gt; 0 and 0 &lt; q &lt; 1 &lt; p &lt; (n + 2)/(n − 2). Under an appropriate growth assumption on a− at infinity, we show that all solutions are compactly supported. When Ω+ = {x ∈ ℝn | a(x) &gt; 0} has several connected components, we prove that there exists an interval on γ in which the solutions exist. In particular, if a(x) = a(|x|), by applying the mountain-pass theorem there are at least two solutions with radial symmetry that are positive in Ω+.

Positive solutions to the singular p-Laplacian BVPs with sign-changing nonlinearities and higher-order derivatives in Banach spaces on time scales

Abstract. In this paper, in order to establish the existence criteria for positive solutions of a multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales, first we prove a fixed point theorem on monotone operators and the Ascoli-Arzela’s theorem on time scales. Then using the monotone operator method, we explore the existence criteria of positive solutions for a general multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales with the singular sign-changing nonlinearities and higher-order derivatives. Finally an example is illustrated to indicate the application of our main results, which generalize some well-known results in the literature.

Second order boundary value problems with sign-changing nonlinearities and nonhomogeneous boundary conditions

The authors consider the boundary value problem with a two-parameter nonhomogeneous multi-point boundary condition \gather u''+g(t)f(t,u)=0, \quad t\in (0,1),\nonumber u(0)=\alpha u(\xi )+\lambda ,\quad u(1)=\beta u(\eta )+\mu .\nonumber \endgather Criteria for the existence of nontrivial solutions of the problem are established. The nonlinear term $f(t,x)$ may take negative values and may be unbounded from below. Conditions are determined by the relationship between the behavior of $f(t, x)/x$ for $x$ near $0$ and $\pm \infty $, and the smallest positive characteristic value of an associated linear integral operator. The analysis mainly relies on topological degree theory. This work complements some recent results in the literature. The results are illustrated with examples.