Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional caseSpringer Science and Business Media LLC - Tập 2016 - Trang 1-11 - 2016
Tongchun Hu, Yongping Sun, Weigang Sun
In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the eff...... hiện toàn bộ
A new kind of double Chebyshev polynomial approximation on unbounded domainsSpringer Science and Business Media LLC - Tập 2013 - Trang 1-13 - 2013
Ayşe Betül Koç, Aydın Kurnaz
In this study, a new solution scheme for the partial differential equations with variable coefficients defined on a large domain, especially including infinities, has been investigated. For this purpose, a spectral basis, called exponential Chebyshev (EC) polynomials, has been extended to a new kind of double Chebyshev polynomials. Many outstanding properties of those polynomials have been shown. ...... hiện toàn bộ
Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operatorSpringer Science and Business Media LLC - Tập 2020 - Trang 1-13 - 2020
Natalia P. Bondarenko
We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account.
Solvability of boundary value problem with p-Laplacian at resonanceSpringer Science and Business Media LLC - Tập 2014 Số 1 - Trang 1-12 - 2014
Jiang, Weihua
By generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence of solutions for p-Laplacian boundary value problems at resonance. An example is given to illustrate our results. MSC:34B15.
Blow-up properties for a degenerate parabolic system coupled via nonlinear boundary fluxSpringer Science and Business Media LLC - Tập 2015 - Trang 1-14 - 2015
Si Xu
In this paper, we study the simultaneous and non-simultaneous blow-up problem for a system of two nonlinear diffusion equations in a bounded interval, coupled at the boundary in a nonlinear way. Under certain hypotheses on the initial data and parameters, we prove that non-simultaneous blow-up is possible. Moreover, we get some conditions on which simultaneous blow-up must occur, as well as the no...... hiện toàn bộ
Nonlinear boundary value problems of a class of elliptic equations involving critical variable exponentsSpringer Science and Business Media LLC - Tập 2019 - Trang 1-21 - 2019
Yingying Shan, Yongqiang Fu
In this paper, we first obtain the existence of solutions for a class of elliptic equations involving critical variable exponents and nonlinear boundary values by the mountain pass theorem and concentration compactness principle. Then, under suitable assumptions, we obtain a sequence of solutions with positive energies going towards infinity by Fountain Theorem.