We consider the Sturm-Liouville operator Lu = u ′′ − q(x)u defined on (0, π) with regular but not strongly regular boundary conditions. Under some supplementary assumptions we prove that the set of potentials q(x) that ensure an asymptotically multiple spectrum is everywhere dense in L 1 (0, π). In the present paper we consider eigenvalue problems for the Sturm-Liouville equation u ′′ − q(x)u +...

*Correspondence: [email protected] Department of Mathematics, Gaziosmanpasa University, Tasliciftlik Campus, Tokat, 60250, Turkey Abstract The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigen...

In this work, byemploying the Leggett-Williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-Laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

in this work, byemploying the leggett-williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

In this paper the existence of unique positive solutions for system (p,q,r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems is established by an application n-fixed point theorem ternary operators on partially ordered metric spaces.

In this paper, we considered the following four-point boundary value problem y Elsevi tion of Enginee J. Zhao) x00ðtÞ þ hðtÞf ðt; xðtÞ; x0ðtÞÞ 1⁄4 0; 0 < t < 1; x0ð0Þ a1xðnÞ 1⁄4 0; x0ð1Þ þ a2xðgÞ 1⁄4 0; where 0 < a1 < n ; 0 < a2 < 1 1 g ; 0 < n < g < 1; a1a2g a1a2n þ a1 þ a2 > 0: By applying fixed-point theorems, we obtain a variety of existence results. In particular, our four-point boundary c...

In this paper, a Sturm–Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that coefficients can be uniquely determined by dense set nodal points. Moreover, we give an algorithm for reconstruction potential function and other in conditions.