# Top PDF Existence of Three Solutions for \$p\$-biharmonic Equation

### Existence of Three Solutions for \$p\$-biharmonic Equation

To the best of our knowledge, there are only very few results regarding multiple solu- tions to the p-biharmonic equation. In this paper, the existence of at least three solutions of problem (P) will be proved. The technical approach is based on the three critical points theorem of B. Ricceri [14]. Our theorem, under the new assumptions, ensures the existence of an open interval Λ ⊆ [0, +∞) and a positive real number ρ such that, for each λ ∈ Λ, problem (P) admits at least three weak solutions whose norms in X are less than ρ.
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### Existence of solutions for nonlinear mixed type integrodifferential equation of second order

Theorem 4. ([5], p-61). Let S be a convex subset of a normed linear space E and assume 0 ∈ S. Let F : S → S be a completely continuous operator, and let ε(F ) = {x ∈ S : x = λF x for some0 < λ < 1}. Then either ε(F ) is unbounded or F has a fixed point.

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### Existence Results for a Second-order Difference Equation with Summation Boundary Conditions at Resonance

[1] V. A. Ilin and E. I. Moiseev, Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, J. Differential Equations 23(1987), 803-810. [2] C. P. Gupta, Solvability of a three-point nonlinear boundary value

### Existence of three solutions for impulsive multi-point boundary value problems

and multiplicity of positive solutions of a boundary value problem for second-order three-point nonlinear impulsive integrodifferential equation of mixed type in a real Banach space. In [32], Liu and Yu with the help of the coincidence degree continuation theorem, achieved a general result concerning the existence of solutions of m-point boundary value problems for second-order differential systems with impulses. They also give a definition of autonomous curvature bound set relative to this m-point boundary value problems, and by using this definition and the above existence theo- rem, obtained some simple existence conditions for solutions of these boundary value problems. Meiqiang and Dongxiu in [14], based on fixed point theory in a cone, dis- cussed the existence of solutions for the m-point BVPs for second-order impulsive differential systems, and Thaiprayoon et al. in [42], introduced a new definition of impulsive conditions for boundary value problems of first-order impulsive differential equations with multi-point boundary conditions was introduced, and used the method of lower and upper solutions in reversed order coupled with the monotone iterative technique to obtain the extremal solutions of the boundary value problem.
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### Solutions of the Polchinski ERG equation in the O(N) scalar model

free massless theory and is called the Gaussian FP (GFP). For all known formulations the ERG equation is stiff and most of its solutions singular at some finite value of the field, making them not acceptable from the physical point of view. Moreover, it turns out that only finitely many solutions of Eq. (2) do not end up in a singularity, thus giving massless continuum limits with the prescribed field content [22]. They correspond to particular values γ = γ ∗ (n) , n = 1, 2, . . ..

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### Braz. J. Phys. vol.38 número2

Now consider those solutions of the equations of motion (5) and (7), which admit constant scalar curvature R. For these solutions, the equation (7) reduces to the equation of motion of the string coordinates, extracted from the Polyakov action with the curved background. However, for general solutions the scalar curvature R depends on the worldsheet coordinates σ and τ, and hence this coincidence does not occur.

### Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

ratio of two polynomials. In addition, a disadvantage not referred can come through: the rational approximation may create inaccurate solutions near its poles when the real solution is not achieved. This drawback advises the search for the optimal order of the Pad´ e approximant to be used, which can be of lower order.

### Eclet. Quím. vol.35 número3

V = − + + − has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N 2 CO and NO

### SUSTAINABLE FINANCING SOLUTIONS FOR THE ROMANIAN HEALTH SYSTEM

)n our opinion the main challenge for the Romanian health care systems is to improve the mix of health care resources doctors, hospital beds, and pharmaceuticals in order to offer greater access to medical services. Romania is still in the process of developing a reform strategy for the health sector. The aim of this reform should be an increasing role of private sector in health care. The reform measures should include:

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### Traveling wave solutions of a biological reaction-convection-diffusion equation model by using \$(G'/G)\$ expansion method

expansion method is quiet efficient and well suited for finding exact solutions. The reliability of the method and reduction in the size of computational domain give this method a wider applicability. With the aid of Maple and by putting them back into the original equation, we have assured the correctness of the obtained solutions. Finally, it is worthwhile to mention that the method is straightforward and concise and it can be applied to other nonlinear evolution equations in engineering and the physical sciences.

### Deciphering the Contribution of Biofilm to the Pathogenesis of Peritoneal Dialysis Infections: Characterization and Microbial Behaviour on Dialysis Fluids

Fig 2. Microbial yield on PD catheters external (A) and intraperitoneal (B) segments and subcutaneous (C) and deep (D) cuffs in patients with and without infection. Data is presented as colony-forming units (CFU)/segment with the corresponding microorganisms represented by specific symbols. dot, coagulase negative Staphylococci (including Staphylococcus epidermidis, S. haemolyticus, S. caprae/ capitis, S. hominis, S. auricularis); diamond filled, Staphylococcus aureus; square filled, Corynebacterium spp.; down-pointing triangle filled, Micrococcus luteus; up- pointing triangle filled, Enterococcus faecalis; hexagon filled, Streptococcus spp.; right-pointing triangle filled, Bacillus spp.; circle, Pseudomonas aeruginosa; square, Sphingomonas spp.; diamond, Alcaligenes faecalis; down-pointing triangle, Serratia marcescens; up-pointing triangle, Burkholderia sp.; left-pointing triangle, Stenotrophomonas maltophilia; right-pointing triangle, Escherichia coli; crossed out circle, Enterobacter aerogenes; star, Candida parapsilosis; asterisk, Candida glabrata; circle quartered, non-identified microorganism. Absence of microorganisms is represented by, vertical line. Polymicrobial cultures are identified with a half tick-up line. In the group “infection” the cause of removal is indicated as alpha, for refractory peritonitis; beta, for relapsing peritonitis; gamma, fungal peritonitis; delta, for catheter-related peritonitis and epsilon, for chronic catheter infections. The dashed line indicates the culture method detection limit.
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### TEMA (São Carlos) vol.17 número1

Existence of Solutions for Optimal Control Problems on Time Scales whose States are Absolutely Continuous.. I.L.D.[r]

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### New multi-soliton solutions for generalized Burgers-Huxley equation

This equation can be solved by various analytical methods, such as the variational iteration method [2], the homotopy perturbation method [3-5], and the exp-function method [6, 7]. A complete review on various analytical method is available in [8, 9]. In this paper the double exp-function method [10] is adopted to elucidate the different velocities and different frequencies in the travelling wave.

[r]

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### On The Existence Of Conditions Of a Classical Solution Of BGK-Poisson's Equation In Finite Time

We study the initial value problem of BGK model [1] coupled with Poisson’s equation, which is a simple relax- ation model introduced by Bhatnagar, Gross & Krook to mimic Boltzmann flows, where f (x, v, t) is the density of plasma particles at time t in the space of position x and velocity v, and φ(x, t) is the potential of electric field of the plasma.

### On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

for some positive constant M . Hence (Aϕ) is equicontinuous. Then by the Ascoli-Arzelà theorem we obtain that A is a compact map. Due to the continuity of all the terms in (2.16), we have that A is continuous. This completes the proof. Theorem 3.4. Let α, β and γ be given by (2.10). Suppose that conditions (2.1)–(2.4), (2.11)–(2.15) hold, then equation (1.1) has a positive periodic solution z satisfying K ≤ z ≤ L.

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### Simple but accurate periodic solutions for the nonlinear pendulum equation

The simple pendulum is a prototype for the study of nonlinear systems and their stability [1]. In fact, pendu- lar oscillations arise in distinct fields of physical science and technology, e.g. acoustic vibrations [2], molecular oscillations [3], optically torqued nanorods [4], Joseph- son superconducting junctions [3, 5], elliptic filters in electronics [6], gravitational lensing [7], smetic C liquid crystals [8], advanced field theory [9], oscillations of build- ings in earthquakes [10], etc. In the small-angle regime, the approximation sin θ ≈ θ works and the equation of motion can be linearized, becoming solvable in terms of a sinusoidal function of time. Beyond this regime, the nonlinear nature of the pendulum motion becomes apparent: (i) the period increases with the amplitude; and (ii) the function θ(t) departs more and more from a harmonic behavior. In the nonlinear regime, the sim- plicity of the sinusoidal solution is lost and the equation of motion becomes unsolvable in terms of elementary functions, so either a direct numerical solution or some analytical approximation is demanded. However, numeri- cal solutions for the pendulum equation loose accuracy
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### Multiplicidade de soluções positivas para algumas classes de problemas elípticos em R2 com condição de Neumann

In this work, we prove the existence and multiplicity of positive weak solutions for some classes of elliptic problems in plane involving exponential growth of the Trudinger-Moser type with Neumann boundary condition. To do this, we use the method of sub and supersolution in combination with variational methods and the maximum principle.

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### On a nonlocal degenerate parabolic problem

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved.

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### An Exact Mapping from Navier-Stokes Equation to Schrodinger Equation via Riccati EquationAn Exact Mapping from Navier-Stokes Equation to Schrodinger Equation via Riccati Equation

This is an alternative version of biquaternionic Schr¨o- dinger representation of Navier-Stokes equations. Numerical solution of the new Navier-Stokes-Schr¨odinger equation (14) can be performed in the same way with [12] using Maxima software package [7], therefore it will not be discussed here.