Existence of Solutions of Nonlinear m-Point Boundary-Value Problems☆

By Ruyun Ma, Nelson Castañeda. 2001

224 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c2aed4940f5c15033fc11730a48494b870a4d773

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations (2009, methodology): “[14], by use of the fixed point theory in a cone, this article is devoted to study m-point BVPs for second-order impulsive differential systems.”
Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. (2002, background): “6 Concluding remarks The multi-point boundary conditions for the problem considered in [19] are special cases of the conditions x′(0) = − k ∑”
NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS (2006, background): “Several such non-local problems have been extensively studied recently, see for example [6, 7, 13, 15, 19] and the papers cited therein.”
Positive solutions for systems of m‐point nonlinear boundary value problems (2008, unknown): “1) with the following boundary conditions ([21]): u(0) = m−2 ∑ i=1 aiu (ξi), u(1) = m−2 ∑ i=1 aiu(ξi), v(0) = m−2 ∑ i=1 aiv (ξi), v(1) = m−2 ∑ i=1 aiv(ξi), (4.”
Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach (2006, background): “This does, in fact, give some completely new results, as we study more general BCs than [16, 21] who studied the multipoint case with positive coefficients and β[u] = 0, (although [16] does not consider positive solutions and allows f(t, u) to have a singularity when u = 0 in one result), and [2, 26”
Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type (2006, background): “Some other authors have made the stronger assumptions that f is either sub- or super-linear, for example [19], [20].”
Positive solutions of nonlocal boundary value problems involving integral conditions (2008, background): “A more general set of BCs for m-point BVPS has been studied in [12, 16], the former allowing singularities in f in the u variable.”
Loss of positivity in a nonlinear scalar heat equation (2006, background): “The problem we discuss is an example of a so called three-point BVP, several such non-local problems have been extensively studied recently, for example [4, 6, 7, 8, 10 , 11] and papers cited therein.”
Multiple sign-changing solutions for some m-point boundary-value problems. (2004, methodology): “Recently, there is much attention focused on the existence of nontrivial or positive solutions of the nonlinear multi-point boundary-value problems(see [3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17] and the references therein).”