Solvability Criteria for Second Order Generalized Sturm–Liouville Problems at Resonance
نویسندگان
چکیده
This paper presents some solvability criteria for the second order nonlinear equation (p(t)u′(t))′ − q(t)u(t) = f ( t, ∫ t 0 u(s)ds, u′(t) ) , t ∈ (0, 1), with one of the following boundary conditions au(0)− bp(0)u′(0) = 0, cu(1) + dp(1)u′(1) = μ1u(ξ), au(0)− bp(0)u′(0) = μ2u(ξ), cu(1) + dp(1)u′(1) = 0, au(0)− bp(0)u′(0) = μ1u(ξ), cu(1) + dp(1)u′(1) = μ2u(ξ). Under the appropriate nonlinear restriction of nonlinearity, solvability criteria for generalized Sturm–Liouville boundary value problems at resonance are established by means of coincidence degree theory of Mawhin type. AMS Subject Classifications: 34B15.
منابع مشابه
Positive solutions for nonlinear systems of third-order generalized sturm-liouville boundary value problems with $(p_1,p_2,ldots,p_n)$-laplacian
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...
متن کاملThe Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points
In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.
متن کاملExistence of multiple solutions for Sturm-Liouville boundary value problems
In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.
متن کاملAsymptotic distributions of Neumann problem for Sturm-Liouville equation
In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.
متن کاملStudies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
Abstract. The Sturm-Liouville boundary value problem of the multi-order fractional differential equation is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.
متن کامل