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Existence of positive solutions for a third-order multipoint boundary value problem and extension to fractional case
Springer 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
On explicit and numerical solvability of parabolic initial-boundary value problems
Springer Science and Business Media LLC - Tập 2006 - Trang 1-12 - 2006
Alexander Kozhevnikov, Olga Lepsky
A homogeneous boundary condition is constructed for the parabolic equation in an arbitrary cylindrical domain ( being a bounded domain, ...... hiện toàn bộ
On an electrorheological fluid equation with orientated convection term
Springer Science and Business Media LLC - Tập 2019 Số 1 - 2019
Huashui Zhan
A new kind of double Chebyshev polynomial approximation on unbounded domains
Springer 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 operator
Springer 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.
Existence and uniqueness of solutions for the second order periodic-integrable boundary value problem
Springer Science and Business Media LLC - Tập 2017 - Trang 1-13 - 2017
Xue Feng, Fuzhong Cong
This paper is mainly devoted to studying one kind of the second order differential equation. Under periodic-integrable boundary value condition, the existence of the solutions of this equation is discussed by the method of the operator theory and the Schauder fixed point theorem.
Solvability of boundary value problem with p-Laplacian at resonance
Springer 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 flux
Springer 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
Sharp criteria of blow-up solutions for the cubic nonlinear beam equation
Springer Science and Business Media LLC - Tập 2019 - Trang 1-8 - 2019
Jun Qing, Chuangyuan Zhang
In this paper, we obtain the precisely sharp criteria of blow-up and global existence for the cubic nonlinear beam equation in the $H^{2}$ energy-critical and ...... hiện toàn bộ
Nonlinear boundary value problems of a class of elliptic equations involving critical variable exponents
Springer 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.
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