Positive Solutions For Eigenvalue Problem Research Articles

Positive solutions for eigenvalue problems of fractional q-difference equation with \u03d5-Laplacian

The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for this problem by means of the Green function and Guo–Krasnoselskii fixed point theorem on cones. Finally, we give some examples to illustrate the use of our results.

Positive solutions for eigenvalue problem of non-linear fractional differential equations

In this paper, by using the fixed point theorem of cone expansion and compression of norm type and monotone iterative technique, we study the eigenvalue problem of non-linear fractional differential equations. The existence and iteration of positive solutions are obtained.

Positive solutions for eigenvalue problem of non-linear fractional differential equations

Positive solutions for eigenvalue problem of non-linear fractional differential equations

Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian

In this paper, we investigate the existence of positive solutions for the eigenvalue problem of nonlinear fractional differential equation with generalized p-Laplacian operatorD0+β(ϕ(D0+αu(t)))=λf(u(t)),0<t<1,u(0)=u′(0)=u′(1)=0,ϕ(D0+αu(0))=(ϕ(D0+αu(1)))′=0,where 2<α⩽3,1<β⩽2 are real numbers, D0+α,D0+β are the standard Riemann–Liouville fractional derivatives, ϕ is a generalized p-Laplacian operator, λ>0 is a parameter, and f:(0,+∞)→(0,+∞) is continuous. By using the properties of Green function and Guo–Krasnosel’skii fixed-point theorem on cones, several new existence results of at least one or two positive solutions in terms of different eigenvalue interval are obtained. Moreover, the nonexistence of positive solution in term of the parameter λ is also considered.

Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations

In this article, by using the fixed point theorem, existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations D 0 + α u ( t ) + λ a ( t ) f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = 0 is considered, where 1 < α < 2 is a real number, D 0 + α is the standard Riemann-Liouville derivate, λ is a positive parameter and a(t) ∈ C([0, 1], [0, ∞)), f(t, u) ∈ C([0, 1] × [0, ∞), [0, ∞)).MSC(2010): 34B18.

Multiple Positive Solutions for Eigenvalue Problems of Hemivariational Inequalities

We study a nonlinear eigenvalue problem with a nonsmooth potential. The subgradients of the potential are only positive near the origin (from above) and near +∞. Also the subdifferential is not necessarily monotone (i.e. the potential is not convex). Using variational techniques and the method of upper and lower solutions, we establish the existence of at least two strictly positive smooth solutions for all the parameters in an interval. Our approach uses the nonsmooth critical point theory for locally Lipschitz functions. A byproduct of our analysis is a generalization of a result of Brezis-Nirenberg (CRAS, 317 (1993)) on H10 versus C10 minimizers of a C1-functional.

Existence results for time scale boundary value problem

In this paper, we establish some existence results for positive solutions to a class of singular boundary value problem on time scale by using the Krasnosel'skii fixed point theorem. Two examples are presented as applications. The conditions we used in this paper are different from those in [D.R. Anderson, Eigenvalue intervals for a two-point boundary value problem on a measure chain, J. Comput. Appl. Math. 141 (2002) 57–64; C.J. Chyan, J. Henderson, Eigenvalues problems for nonlinear differential equations on a measure chain, J. Math. Anal. Appl. 245 (2000) 547–559; L.H. Erbe, A. Peterson Positive solutions for nonlinear differential equation on a measure chain, Math. Comput. Modelling 32 (2000) 571–585; L.H. Erbe, H.Y. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994) 743–748; J. Henderson, H.Y. Wang, Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl. 208 (1997) 252–259; C.H. Hong, C.C. Yeh, Positive solutions for eigenvalue problems on a measure chain, Nonlinear Anal. 51 (2002) 499–507; W.C. Lian; W.F. Wong; C.C. Yeh, On the existence of positive solutions of nonlinear differential equations, Proc. Amer. Math. Soc. 124 (1996) 1117–1126; J. Liang, T.J. Xiao, Z.C. Hao, Positive solutions of singular differential equations on measure chain, Comput. Math. Appl. 49 (2005) 651–663].

Positive solutions for Eigenvalue problems of fourth-order elastic beam equations

In this paper, we investigate the positive solutions of equations w (4)(t) = λƒ(t,w(t)) with w(0) = w(1) = w′(0) = w′(1) = 0. We obtain several existence and multiplicity results by an application of the Krasnosel'skii fixed-point theorem of cone expansion-compression type. This class of equations usually describes the deformations of elastic beams with fixed both endpoints.

Positive solutions for Eigenvalue problems on a measure chain

Positive solutions for Eigenvalue problems on a measure chain