Multiple positive solutions for singular BVPs on the positive half-line

Unbounded solutions of BVP for second order ODE with p-Laplacian on the half line

“…In our derivation, the cone needed has to be very technically constructed -this is so since the boundary value problem involves the nonlinear operator [̺ϕ(x ′ )] ′ and the possible solutions are not concave if ̺ ≡ 1, hence the cone cannot be constructed by using the concavity of x or even the Green function. Our result improves and complements the work of [1][2][3][4][5][6][7], . The paper is organized as follows.…”

“…Recently there has been increasing interest in the existence of positive solutions of boundary value problems (BVP) for differential equations on the half lines, see the references [1][2][3][4][5][6][7], . Fixed point theorems have been useful in establishing the existence of positive solutions.…”

“…We note that Example 4.1 cannot be covered by the theorems in [5], [10], [14], [15], [17][18][19][20][21], [23][24][25][26], [29] since the nonlinear operator [x ′ ] 3 appears in (4.1), the first boundary condition in (4.1) is of integral type and both the conditions in (4.1) are non-homogeneous boundary conditions while x ′ (∞) = 0 is contained in Authors' addresses: Yuji Liu, Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, P. R. China, e-mail: liuyuji888@sohu.com; Patricia J. Y. Wong, School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore, e-mail: ejywong@ntu.edu.sg.…”

Multiple solutions for a BVP on $${(0,+\infty)}$$ ( 0 , + ∞ ) via Morse theory and $${H^1_{0,p}(\mathbb{R}^+)}$$ H 0 , p 1 ( R + ) versus $${C^1_{p}(\mathbb{R}^+)}$$ C p 1 ( R + ) local minimizers

“…In particular, second-order boundary value problems can be considered as interesting models both from the mathematical and the physical points of view. Regarding the recent mathematical results for BVPs set on unbounded domains, we refer the reader to, e.g., [12][13][14], and the references therein. The behavior of the nonlinearity involved in the ordinary differential equation, which refers to the physical source term, represents the main difficulty when dealing with such BVPs: several methods have been employed so far such that iterative and topological methods as well as techniques based on monotonicity and comparison principles.…”

UPPER AND LOWER SOLUTIONS FOR Φ-LAPLACIAN THIRD-ORDER BVPs ON THE HALF LINE

“…In the last couple of years, the mathematical investigation of such problems, especially second-order boundary value problems have attracted several authors (see, e.g., [4], [5], [6], [7], [8], [9] and the references therein). However, only some of them were interested in higher-order differential equations on [0, +∞) (see [9], [11], [12]).…”